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<h1 class="epydoc">Source Code for <a href="dadi.Integration-module.html">Module dadi.Integration</a></h1>
<pre class="py-src">
<a name="L1"></a><tt class="py-lineno">  1</tt>  <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L2"></a><tt class="py-lineno">  2</tt>  <tt class="py-line"><tt class="py-docstring">Functions for integrating population frequency spectra.</tt> </tt>
<a name="L3"></a><tt class="py-lineno">  3</tt>  <tt class="py-line"><tt class="py-docstring">"""</tt> </tt>
<a name="L4"></a><tt class="py-lineno">  4</tt>  <tt class="py-line"> </tt>
<a name="L5"></a><tt class="py-lineno">  5</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">logging</tt> </tt>
<a name="L6"></a><tt class="py-lineno">  6</tt>  <tt class="py-line"><tt id="link-0" class="py-name" targets="Variable dadi.Hessian.logger=dadi.Hessian-module.html#logger,Variable dadi.Inference.logger=dadi.Inference-module.html#logger,Variable dadi.Integration.logger=dadi.Integration-module.html#logger,Variable dadi.Numerics.logger=dadi.Numerics-module.html#logger,Variable dadi.RunInParallel.logger=dadi.RunInParallel-module.html#logger,Variable dadi.Spectrum_mod.logger=dadi.Spectrum_mod-module.html#logger"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-0', 'logger', 'link-0');">logger</a></tt> <tt class="py-op">=</tt> <tt class="py-name">logging</tt><tt class="py-op">.</tt><tt class="py-name">getLogger</tt><tt class="py-op">(</tt><tt class="py-string">'Integration'</tt><tt class="py-op">)</tt> </tt>
<a name="L7"></a><tt class="py-lineno">  7</tt>  <tt class="py-line"> </tt>
<a name="L8"></a><tt class="py-lineno">  8</tt>  <tt class="py-line"><tt class="py-comment">#</tt> </tt>
<a name="L9"></a><tt class="py-lineno">  9</tt>  <tt class="py-line"><tt class="py-comment"># Note that these functions have all be written for xx=yy=zz, so the grids are</tt> </tt>
<a name="L10"></a><tt class="py-lineno"> 10</tt>  <tt class="py-line"><tt class="py-comment"># identical in each direction. That's not essential here, though. The reason we</tt> </tt>
<a name="L11"></a><tt class="py-lineno"> 11</tt>  <tt class="py-line"><tt class="py-comment"># do it is because later we'll want to extrapolate, and it's not obvious how to</tt> </tt>
<a name="L12"></a><tt class="py-lineno"> 12</tt>  <tt class="py-line"><tt class="py-comment"># do so if the grids differ.</tt> </tt>
<a name="L13"></a><tt class="py-lineno"> 13</tt>  <tt class="py-line"><tt class="py-comment">#</tt> </tt>
<a name="L14"></a><tt class="py-lineno"> 14</tt>  <tt class="py-line"> </tt>
<a name="L15"></a><tt class="py-lineno"> 15</tt>  <tt class="py-line"><tt class="py-comment">#: Controls use of Chang and Cooper's delj trick, which seems to lower accuracy.</tt> </tt>
<a name="L16"></a><tt class="py-lineno"> 16</tt>  <tt class="py-line"><tt id="link-1" class="py-name" targets="Variable dadi.Integration.use_delj_trick=dadi.Integration-module.html#use_delj_trick"><a title="dadi.Integration.use_delj_trick" class="py-name" href="#" onclick="return doclink('link-1', 'use_delj_trick', 'link-1');">use_delj_trick</a></tt> <tt class="py-op">=</tt> <tt class="py-name">False</tt> </tt>
<a name="L17"></a><tt class="py-lineno"> 17</tt>  <tt class="py-line"> </tt>
<a name="L18"></a><tt class="py-lineno"> 18</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt class="py-name">numpy</tt> </tt>
<a name="L19"></a><tt class="py-lineno"> 19</tt>  <tt class="py-line"><tt class="py-keyword">from</tt> <tt class="py-name">numpy</tt> <tt class="py-keyword">import</tt> <tt class="py-name">newaxis</tt> <tt class="py-keyword">as</tt> <tt class="py-name">nuax</tt> </tt>
<a name="L20"></a><tt class="py-lineno"> 20</tt>  <tt class="py-line"> </tt>
<a name="L21"></a><tt class="py-lineno"> 21</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt id="link-2" class="py-name" targets="Module dadi.Misc=dadi.Misc-module.html"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-2', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">,</tt> <tt id="link-3" class="py-name" targets="Module dadi.Numerics=dadi.Numerics-module.html"><a title="dadi.Numerics" class="py-name" href="#" onclick="return doclink('link-3', 'Numerics', 'link-3');">Numerics</a></tt><tt class="py-op">,</tt> <tt id="link-4" class="py-name" targets="Module dadi.tridiag=dadi.tridiag-module.html,Variable dadi.tridiag.tridiag=dadi.tridiag-module.html#tridiag"><a title="dadi.tridiag
dadi.tridiag.tridiag" class="py-name" href="#" onclick="return doclink('link-4', 'tridiag', 'link-4');">tridiag</a></tt> </tt>
<a name="L22"></a><tt class="py-lineno"> 22</tt>  <tt class="py-line"><tt class="py-keyword">import</tt> <tt id="link-5" class="py-name" targets="Module dadi.integration_c=dadi.integration_c-module.html"><a title="dadi.integration_c" class="py-name" href="#" onclick="return doclink('link-5', 'integration_c', 'link-5');">integration_c</a></tt> <tt class="py-keyword">as</tt> <tt class="py-name">int_c</tt> </tt>
<a name="L23"></a><tt class="py-lineno"> 23</tt>  <tt class="py-line"> </tt>
<a name="L24"></a><tt class="py-lineno"> 24</tt>  <tt class="py-line"><tt class="py-comment">#: Controls timestep for integrations. This is a reasonable default for</tt> </tt>
<a name="L25"></a><tt class="py-lineno"> 25</tt>  <tt class="py-line"><tt class="py-comment">#: gridsizes of ~60. See set_timescale_factor for better control.</tt> </tt>
<a name="L26"></a><tt class="py-lineno"> 26</tt>  <tt class="py-line"><tt id="link-6" class="py-name" targets="Variable dadi.Integration.timescale_factor=dadi.Integration-module.html#timescale_factor"><a title="dadi.Integration.timescale_factor" class="py-name" href="#" onclick="return doclink('link-6', 'timescale_factor', 'link-6');">timescale_factor</a></tt> <tt class="py-op">=</tt> <tt class="py-number">1e-3</tt> </tt>
<a name="L27"></a><tt class="py-lineno"> 27</tt>  <tt class="py-line"> </tt>
<a name="L28"></a><tt class="py-lineno"> 28</tt>  <tt class="py-line"><tt class="py-comment">#: Whether to use old timestep method, which is old_timescale_factor * dx[0].</tt> </tt>
<a name="L29"></a><tt class="py-lineno"> 29</tt>  <tt class="py-line"><tt id="link-7" class="py-name" targets="Variable dadi.Integration.use_old_timestep=dadi.Integration-module.html#use_old_timestep"><a title="dadi.Integration.use_old_timestep" class="py-name" href="#" onclick="return doclink('link-7', 'use_old_timestep', 'link-7');">use_old_timestep</a></tt> <tt class="py-op">=</tt> <tt class="py-name">False</tt> </tt>
<a name="L30"></a><tt class="py-lineno"> 30</tt>  <tt class="py-line"><tt class="py-comment">#: Factor for told timestep method.</tt> </tt>
<a name="L31"></a><tt class="py-lineno"> 31</tt>  <tt class="py-line"><tt id="link-8" class="py-name" targets="Variable dadi.Integration.old_timescale_factor=dadi.Integration-module.html#old_timescale_factor"><a title="dadi.Integration.old_timescale_factor" class="py-name" href="#" onclick="return doclink('link-8', 'old_timescale_factor', 'link-8');">old_timescale_factor</a></tt> <tt class="py-op">=</tt> <tt class="py-number">0.1</tt> </tt>
<a name="L32"></a><tt class="py-lineno"> 32</tt>  <tt class="py-line"> </tt>
<a name="set_timescale_factor"></a><div id="set_timescale_factor-def"><a name="L33"></a><tt class="py-lineno"> 33</tt> <a class="py-toggle" href="#" id="set_timescale_factor-toggle" onclick="return toggle('set_timescale_factor');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#set_timescale_factor">set_timescale_factor</a><tt class="py-op">(</tt><tt class="py-param">pts</tt><tt class="py-op">,</tt> <tt class="py-param">factor</tt><tt class="py-op">=</tt><tt class="py-number">10</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="set_timescale_factor-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="set_timescale_factor-expanded"><a name="L34"></a><tt class="py-lineno"> 34</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L35"></a><tt class="py-lineno"> 35</tt>  <tt class="py-line"><tt class="py-docstring">    Controls the fineness of timesteps during integration.</tt> </tt>
<a name="L36"></a><tt class="py-lineno"> 36</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L37"></a><tt class="py-lineno"> 37</tt>  <tt class="py-line"><tt class="py-docstring">    The timestep will be proportional to Numerics.default_grid(pts)[1]/factor.</tt> </tt>
<a name="L38"></a><tt class="py-lineno"> 38</tt>  <tt class="py-line"><tt class="py-docstring">    Typically, pts should be set to the *largest* number of grid points used in</tt> </tt>
<a name="L39"></a><tt class="py-lineno"> 39</tt>  <tt class="py-line"><tt class="py-docstring">    extrapolation. </tt> </tt>
<a name="L40"></a><tt class="py-lineno"> 40</tt>  <tt class="py-line"><tt class="py-docstring">    </tt> </tt>
<a name="L41"></a><tt class="py-lineno"> 41</tt>  <tt class="py-line"><tt class="py-docstring">    An adjustment factor of 10 typically results in acceptable accuracy. It may</tt> </tt>
<a name="L42"></a><tt class="py-lineno"> 42</tt>  <tt class="py-line"><tt class="py-docstring">    be desirable to increase this factor, particularly when population sizes</tt> </tt>
<a name="L43"></a><tt class="py-lineno"> 43</tt>  <tt class="py-line"><tt class="py-docstring">    are changing continously and rapidly.</tt> </tt>
<a name="L44"></a><tt class="py-lineno"> 44</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L45"></a><tt class="py-lineno"> 45</tt>  <tt class="py-line">    <tt class="py-comment"># Implementation note: This cannot be easily be set automatically, because</tt> </tt>
<a name="L46"></a><tt class="py-lineno"> 46</tt>  <tt class="py-line">    <tt class="py-comment"># the integration doesn't know whether its results will be used in an</tt> </tt>
<a name="L47"></a><tt class="py-lineno"> 47</tt>  <tt class="py-line">    <tt class="py-comment"># extrapolation.</tt> </tt>
<a name="L48"></a><tt class="py-lineno"> 48</tt>  <tt class="py-line">    <tt class="py-keyword">global</tt> <tt id="link-9" class="py-name"><a title="dadi.Integration.timescale_factor" class="py-name" href="#" onclick="return doclink('link-9', 'timescale_factor', 'link-6');">timescale_factor</a></tt> </tt>
<a name="L49"></a><tt class="py-lineno"> 49</tt>  <tt class="py-line">    <tt id="link-10" class="py-name"><a title="dadi.Hessian.logger
dadi.Inference.logger
dadi.Integration.logger
dadi.Numerics.logger
dadi.RunInParallel.logger
dadi.Spectrum_mod.logger" class="py-name" href="#" onclick="return doclink('link-10', 'logger', 'link-0');">logger</a></tt><tt class="py-op">.</tt><tt class="py-name">warn</tt><tt class="py-op">(</tt><tt class="py-string">'set_timescale_factor has been deprecated, as it may be too '</tt> </tt>
<a name="L50"></a><tt class="py-lineno"> 50</tt>  <tt class="py-line">                <tt class="py-string">'conservative (and thus slow) in choosing timesteps. If you '</tt> </tt>
<a name="L51"></a><tt class="py-lineno"> 51</tt>  <tt class="py-line">                <tt class="py-string">'wish to take smaller timesteps for accuracy (particularly for '</tt> </tt>
<a name="L52"></a><tt class="py-lineno"> 52</tt>  <tt class="py-line">                <tt class="py-string">'a very quickly growing population), manually set '</tt> </tt>
<a name="L53"></a><tt class="py-lineno"> 53</tt>  <tt class="py-line">                <tt class="py-string">'dadi.Integration.timescale_factor to a smaller value. '</tt> </tt>
<a name="L54"></a><tt class="py-lineno"> 54</tt>  <tt class="py-line">                <tt class="py-string">'(Current value is %g.)'</tt> <tt class="py-op">%</tt> <tt id="link-11" class="py-name"><a title="dadi.Integration.timescale_factor" class="py-name" href="#" onclick="return doclink('link-11', 'timescale_factor', 'link-6');">timescale_factor</a></tt><tt class="py-op">)</tt> </tt>
<a name="L55"></a><tt class="py-lineno"> 55</tt>  <tt class="py-line">    <tt id="link-12" class="py-name"><a title="dadi.Integration.timescale_factor" class="py-name" href="#" onclick="return doclink('link-12', 'timescale_factor', 'link-6');">timescale_factor</a></tt> <tt class="py-op">=</tt> <tt id="link-13" class="py-name"><a title="dadi.Numerics" class="py-name" href="#" onclick="return doclink('link-13', 'Numerics', 'link-3');">Numerics</a></tt><tt class="py-op">.</tt><tt class="py-name">default_grid</tt><tt class="py-op">(</tt><tt class="py-name">pts</tt><tt class="py-op">)</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-name">factor</tt> </tt>
</div><a name="L56"></a><tt class="py-lineno"> 56</tt>  <tt class="py-line"> </tt>
<a name="_inject_mutations_1D"></a><div id="_inject_mutations_1D-def"><a name="L57"></a><tt class="py-lineno"> 57</tt> <a class="py-toggle" href="#" id="_inject_mutations_1D-toggle" onclick="return toggle('_inject_mutations_1D');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_inject_mutations_1D">_inject_mutations_1D</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">dt</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_inject_mutations_1D-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_inject_mutations_1D-expanded"><a name="L58"></a><tt class="py-lineno"> 58</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L59"></a><tt class="py-lineno"> 59</tt>  <tt class="py-line"><tt class="py-docstring">    Inject novel mutations for a timestep.</tt> </tt>
<a name="L60"></a><tt class="py-lineno"> 60</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L61"></a><tt class="py-lineno"> 61</tt>  <tt class="py-line">    <tt class="py-name">phi</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dt</tt><tt class="py-op">/</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">theta0</tt><tt class="py-op">/</tt><tt class="py-number">2</tt> <tt class="py-op">*</tt> <tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L62"></a><tt class="py-lineno"> 62</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="_inject_mutations_2D"></a><div id="_inject_mutations_2D-def"><a name="L63"></a><tt class="py-lineno"> 63</tt> <a class="py-toggle" href="#" id="_inject_mutations_2D-toggle" onclick="return toggle('_inject_mutations_2D');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_inject_mutations_2D">_inject_mutations_2D</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">dt</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">yy</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">,</tt> <tt class="py-param">frozen1</tt><tt class="py-op">,</tt> <tt class="py-param">frozen2</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_inject_mutations_2D-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_inject_mutations_2D-expanded"><a name="L64"></a><tt class="py-lineno"> 64</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L65"></a><tt class="py-lineno"> 65</tt>  <tt class="py-line"><tt class="py-docstring">    Inject novel mutations for a timestep.</tt> </tt>
<a name="L66"></a><tt class="py-lineno"> 66</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L67"></a><tt class="py-lineno"> 67</tt>  <tt class="py-line">    <tt class="py-comment"># Population 1</tt> </tt>
<a name="L68"></a><tt class="py-lineno"> 68</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen1</tt><tt class="py-op">:</tt> </tt>
<a name="L69"></a><tt class="py-lineno"> 69</tt>  <tt class="py-line">        <tt class="py-name">phi</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dt</tt><tt class="py-op">/</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">theta0</tt><tt class="py-op">/</tt><tt class="py-number">2</tt> <tt class="py-op">*</tt> <tt class="py-number">4</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L70"></a><tt class="py-lineno"> 70</tt>  <tt class="py-line">    <tt class="py-comment"># Population 2</tt> </tt>
<a name="L71"></a><tt class="py-lineno"> 71</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen2</tt><tt class="py-op">:</tt> </tt>
<a name="L72"></a><tt class="py-lineno"> 72</tt>  <tt class="py-line">        <tt class="py-name">phi</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dt</tt><tt class="py-op">/</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">theta0</tt><tt class="py-op">/</tt><tt class="py-number">2</tt> <tt class="py-op">*</tt> <tt class="py-number">4</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L73"></a><tt class="py-lineno"> 73</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="_inject_mutations_3D"></a><div id="_inject_mutations_3D-def"><a name="L74"></a><tt class="py-lineno"> 74</tt> <a class="py-toggle" href="#" id="_inject_mutations_3D-toggle" onclick="return toggle('_inject_mutations_3D');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_inject_mutations_3D">_inject_mutations_3D</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">dt</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">yy</tt><tt class="py-op">,</tt> <tt class="py-param">zz</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">,</tt> <tt class="py-param">frozen1</tt><tt class="py-op">,</tt> <tt class="py-param">frozen2</tt><tt class="py-op">,</tt> <tt class="py-param">frozen3</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_inject_mutations_3D-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_inject_mutations_3D-expanded"><a name="L75"></a><tt class="py-lineno"> 75</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L76"></a><tt class="py-lineno"> 76</tt>  <tt class="py-line"><tt class="py-docstring">    Inject novel mutations for a timestep.</tt> </tt>
<a name="L77"></a><tt class="py-lineno"> 77</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L78"></a><tt class="py-lineno"> 78</tt>  <tt class="py-line">    <tt class="py-comment"># Population 1</tt> </tt>
<a name="L79"></a><tt class="py-lineno"> 79</tt>  <tt class="py-line">    <tt class="py-comment"># Normalization based on the multi-dimensional trapezoid rule is </tt> </tt>
<a name="L80"></a><tt class="py-lineno"> 80</tt>  <tt class="py-line">    <tt class="py-comment"># implemented                      ************** here ***************</tt> </tt>
<a name="L81"></a><tt class="py-lineno"> 81</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen1</tt><tt class="py-op">:</tt> </tt>
<a name="L82"></a><tt class="py-lineno"> 82</tt>  <tt class="py-line">        <tt class="py-name">phi</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dt</tt><tt class="py-op">/</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">theta0</tt><tt class="py-op">/</tt><tt class="py-number">2</tt> <tt class="py-op">*</tt> <tt class="py-number">8</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L83"></a><tt class="py-lineno"> 83</tt>  <tt class="py-line">    <tt class="py-comment"># Population 2</tt> </tt>
<a name="L84"></a><tt class="py-lineno"> 84</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen2</tt><tt class="py-op">:</tt> </tt>
<a name="L85"></a><tt class="py-lineno"> 85</tt>  <tt class="py-line">        <tt class="py-name">phi</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dt</tt><tt class="py-op">/</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">theta0</tt><tt class="py-op">/</tt><tt class="py-number">2</tt> <tt class="py-op">*</tt> <tt class="py-number">8</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L86"></a><tt class="py-lineno"> 86</tt>  <tt class="py-line">    <tt class="py-comment"># Population 3</tt> </tt>
<a name="L87"></a><tt class="py-lineno"> 87</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen3</tt><tt class="py-op">:</tt> </tt>
<a name="L88"></a><tt class="py-lineno"> 88</tt>  <tt class="py-line">        <tt class="py-name">phi</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dt</tt><tt class="py-op">/</tt><tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">theta0</tt><tt class="py-op">/</tt><tt class="py-number">2</tt> <tt class="py-op">*</tt> <tt class="py-number">8</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L89"></a><tt class="py-lineno"> 89</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="L90"></a><tt class="py-lineno"> 90</tt>  <tt class="py-line"> </tt>
<a name="_compute_dt"></a><div id="_compute_dt-def"><a name="L91"></a><tt class="py-lineno"> 91</tt> <a class="py-toggle" href="#" id="_compute_dt-toggle" onclick="return toggle('_compute_dt');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_compute_dt">_compute_dt</a><tt class="py-op">(</tt><tt class="py-param">dx</tt><tt class="py-op">,</tt> <tt class="py-param">nu</tt><tt class="py-op">,</tt> <tt class="py-param">ms</tt><tt class="py-op">,</tt> <tt class="py-param">gamma</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_compute_dt-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_compute_dt-expanded"><a name="L92"></a><tt class="py-lineno"> 92</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L93"></a><tt class="py-lineno"> 93</tt>  <tt class="py-line"><tt class="py-docstring">    Compute the appropriate timestep given the current demographic params.</tt> </tt>
<a name="L94"></a><tt class="py-lineno"> 94</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L95"></a><tt class="py-lineno"> 95</tt>  <tt class="py-line"><tt class="py-docstring">    This is based on the maximum V or M expected in this direction. The</tt> </tt>
<a name="L96"></a><tt class="py-lineno"> 96</tt>  <tt class="py-line"><tt class="py-docstring">    timestep is scaled such that if the params are rescaled correctly by a</tt> </tt>
<a name="L97"></a><tt class="py-lineno"> 97</tt>  <tt class="py-line"><tt class="py-docstring">    constant, the exact same integration happens. (This is equivalent to</tt> </tt>
<a name="L98"></a><tt class="py-lineno"> 98</tt>  <tt class="py-line"><tt class="py-docstring">    multiplying the eqn through by some other 2N...)</tt> </tt>
<a name="L99"></a><tt class="py-lineno"> 99</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L100"></a><tt class="py-lineno">100</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt id="link-14" class="py-name"><a title="dadi.Integration.use_old_timestep" class="py-name" href="#" onclick="return doclink('link-14', 'use_old_timestep', 'link-7');">use_old_timestep</a></tt><tt class="py-op">:</tt> </tt>
<a name="L101"></a><tt class="py-lineno">101</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-15" class="py-name"><a title="dadi.Integration.old_timescale_factor" class="py-name" href="#" onclick="return doclink('link-15', 'old_timescale_factor', 'link-8');">old_timescale_factor</a></tt> <tt class="py-op">*</tt> <tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L102"></a><tt class="py-lineno">102</tt>  <tt class="py-line"> </tt>
<a name="L103"></a><tt class="py-lineno">103</tt>  <tt class="py-line">    <tt class="py-comment"># These are the maxima for V_func and M_func over the domain</tt> </tt>
<a name="L104"></a><tt class="py-lineno">104</tt>  <tt class="py-line">    <tt class="py-comment"># For h != 0.5, the maximum of M_func is not easy analytically. It is close</tt> </tt>
<a name="L105"></a><tt class="py-lineno">105</tt>  <tt class="py-line">    <tt class="py-comment"># to the 0.5 or 0.25 value, though, so we use those as an approximation.</tt> </tt>
<a name="L106"></a><tt class="py-lineno">106</tt>  <tt class="py-line"> </tt>
<a name="L107"></a><tt class="py-lineno">107</tt>  <tt class="py-line">    <tt class="py-comment"># It might seem natural to scale dt based on dx[0]. However, testing has</tt> </tt>
<a name="L108"></a><tt class="py-lineno">108</tt>  <tt class="py-line">    <tt class="py-comment"># shown that extrapolation is much more reliable when the same timesteps</tt> </tt>
<a name="L109"></a><tt class="py-lineno">109</tt>  <tt class="py-line">    <tt class="py-comment"># are used in evaluations at different grid sizes.</tt> </tt>
<a name="L110"></a><tt class="py-lineno">110</tt>  <tt class="py-line">    <tt class="py-name">maxVM</tt> <tt class="py-op">=</tt> <tt class="py-name">max</tt><tt class="py-op">(</tt><tt class="py-number">0.25</tt><tt class="py-op">/</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">sum</tt><tt class="py-op">(</tt><tt class="py-name">ms</tt><tt class="py-op">)</tt><tt class="py-op">,</tt>\ </tt>
<a name="L111"></a><tt class="py-lineno">111</tt>  <tt class="py-line">                <tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">gamma</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">max</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">h</tt> <tt class="py-op">+</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">h</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">0.5</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-number">0.5</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-number">0.5</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> </tt>
<a name="L112"></a><tt class="py-lineno">112</tt>  <tt class="py-line">                                   <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">abs</tt><tt class="py-op">(</tt><tt class="py-name">h</tt> <tt class="py-op">+</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">h</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">0.25</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-number">0.25</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-number">0.25</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L113"></a><tt class="py-lineno">113</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">maxVM</tt> <tt class="py-op">&gt;</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L114"></a><tt class="py-lineno">114</tt>  <tt class="py-line">        <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt id="link-16" class="py-name"><a title="dadi.Integration.timescale_factor" class="py-name" href="#" onclick="return doclink('link-16', 'timescale_factor', 'link-6');">timescale_factor</a></tt> <tt class="py-op">/</tt> <tt class="py-name">maxVM</tt> </tt>
<a name="L115"></a><tt class="py-lineno">115</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L116"></a><tt class="py-lineno">116</tt>  <tt class="py-line">        <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">inf</tt> </tt>
<a name="L117"></a><tt class="py-lineno">117</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">dt</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L118"></a><tt class="py-lineno">118</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'Timestep is zero. Values passed in are nu=%f, ms=%s,'</tt> </tt>
<a name="L119"></a><tt class="py-lineno">119</tt>  <tt class="py-line">                         <tt class="py-string">'gamma=%f, h=%f.'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">str</tt><tt class="py-op">(</tt><tt class="py-name">ms</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L120"></a><tt class="py-lineno">120</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">dt</tt> </tt>
</div><a name="L121"></a><tt class="py-lineno">121</tt>  <tt class="py-line"> </tt>
<a name="one_pop"></a><div id="one_pop-def"><a name="L122"></a><tt class="py-lineno">122</tt> <a class="py-toggle" href="#" id="one_pop-toggle" onclick="return toggle('one_pop');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#one_pop">one_pop</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">T</tt><tt class="py-op">,</tt> <tt class="py-param">nu</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">gamma</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">=</tt><tt class="py-number">1.0</tt><tt class="py-op">,</tt> <tt class="py-param">initial_t</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt>  </tt>
<a name="L123"></a><tt class="py-lineno">123</tt>  <tt class="py-line">            <tt class="py-param">frozen</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> <tt class="py-param">beta</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="one_pop-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="one_pop-expanded"><a name="L124"></a><tt class="py-lineno">124</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L125"></a><tt class="py-lineno">125</tt>  <tt class="py-line"><tt class="py-docstring">    Integrate a 1-dimensional phi foward.</tt> </tt>
<a name="L126"></a><tt class="py-lineno">126</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L127"></a><tt class="py-lineno">127</tt>  <tt class="py-line"><tt class="py-docstring">    phi: Initial 1-dimensional phi</tt> </tt>
<a name="L128"></a><tt class="py-lineno">128</tt>  <tt class="py-line"><tt class="py-docstring">    xx: Grid upon (0,1) overwhich phi is defined.</tt> </tt>
<a name="L129"></a><tt class="py-lineno">129</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L130"></a><tt class="py-lineno">130</tt>  <tt class="py-line"><tt class="py-docstring">    nu, gamma, and theta0 may be functions of time.</tt> </tt>
<a name="L131"></a><tt class="py-lineno">131</tt>  <tt class="py-line"><tt class="py-docstring">    nu: Population size</tt> </tt>
<a name="L132"></a><tt class="py-lineno">132</tt>  <tt class="py-line"><tt class="py-docstring">    gamma: Selection coefficient on *all* segregating alleles</tt> </tt>
<a name="L133"></a><tt class="py-lineno">133</tt>  <tt class="py-line"><tt class="py-docstring">    h: Dominance coefficient. h = 0.5 corresponds to genic selection. </tt> </tt>
<a name="L134"></a><tt class="py-lineno">134</tt>  <tt class="py-line"><tt class="py-docstring">       Heterozygotes have fitness 1+2sh and homozygotes have fitness 1+2s.</tt> </tt>
<a name="L135"></a><tt class="py-lineno">135</tt>  <tt class="py-line"><tt class="py-docstring">    theta0: Propotional to ancestral size. Typically constant.</tt> </tt>
<a name="L136"></a><tt class="py-lineno">136</tt>  <tt class="py-line"><tt class="py-docstring">    beta: Breeding ratio, beta=Nf/Nm.</tt> </tt>
<a name="L137"></a><tt class="py-lineno">137</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L138"></a><tt class="py-lineno">138</tt>  <tt class="py-line"><tt class="py-docstring">    T: Time at which to halt integration</tt> </tt>
<a name="L139"></a><tt class="py-lineno">139</tt>  <tt class="py-line"><tt class="py-docstring">    initial_t: Time at which to start integration. (Note that this only matters</tt> </tt>
<a name="L140"></a><tt class="py-lineno">140</tt>  <tt class="py-line"><tt class="py-docstring">               if one of the demographic parameters is a function of time.)</tt> </tt>
<a name="L141"></a><tt class="py-lineno">141</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L142"></a><tt class="py-lineno">142</tt>  <tt class="py-line"><tt class="py-docstring">    frozen: If True, population is 'frozen' so that it does not change.</tt> </tt>
<a name="L143"></a><tt class="py-lineno">143</tt>  <tt class="py-line"><tt class="py-docstring">            In the one_pop case, this is equivalent to not running the</tt> </tt>
<a name="L144"></a><tt class="py-lineno">144</tt>  <tt class="py-line"><tt class="py-docstring">            integration at all.</tt> </tt>
<a name="L145"></a><tt class="py-lineno">145</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L146"></a><tt class="py-lineno">146</tt>  <tt class="py-line">    <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L147"></a><tt class="py-lineno">147</tt>  <tt class="py-line"> </tt>
<a name="L148"></a><tt class="py-lineno">148</tt>  <tt class="py-line">    <tt class="py-comment"># For a one population integration, freezing means just not integrating.</tt> </tt>
<a name="L149"></a><tt class="py-lineno">149</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">frozen</tt><tt class="py-op">:</tt> </tt>
<a name="L150"></a><tt class="py-lineno">150</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
<a name="L151"></a><tt class="py-lineno">151</tt>  <tt class="py-line"> </tt>
<a name="L152"></a><tt class="py-lineno">152</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">initial_t</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L153"></a><tt class="py-lineno">153</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
<a name="L154"></a><tt class="py-lineno">154</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">initial_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L155"></a><tt class="py-lineno">155</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'Final integration time T (%f) is less than '</tt> </tt>
<a name="L156"></a><tt class="py-lineno">156</tt>  <tt class="py-line">                         <tt class="py-string">'intial_time (%f). Integration cannot be run '</tt> </tt>
<a name="L157"></a><tt class="py-lineno">157</tt>  <tt class="py-line">                         <tt class="py-string">'backwards.'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">T</tt><tt class="py-op">,</tt> <tt class="py-name">initial_t</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L158"></a><tt class="py-lineno">158</tt>  <tt class="py-line"> </tt>
<a name="L159"></a><tt class="py-lineno">159</tt>  <tt class="py-line">    <tt class="py-name">vars_to_check</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
<a name="L160"></a><tt class="py-lineno">160</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">all</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isscalar</tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">var</tt> <tt class="py-keyword">in</tt> <tt class="py-name">vars_to_check</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L161"></a><tt class="py-lineno">161</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-17" class="py-name" targets="Function dadi.Integration._one_pop_const_params()=dadi.Integration-module.html#_one_pop_const_params"><a title="dadi.Integration._one_pop_const_params" class="py-name" href="#" onclick="return doclink('link-17', '_one_pop_const_params', 'link-17');">_one_pop_const_params</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt><tt class="py-op">,</tt> <tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">,</tt>  </tt>
<a name="L162"></a><tt class="py-lineno">162</tt>  <tt class="py-line">                                     <tt class="py-name">initial_t</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
<a name="L163"></a><tt class="py-lineno">163</tt>  <tt class="py-line"> </tt>
<a name="L164"></a><tt class="py-lineno">164</tt>  <tt class="py-line">    <tt class="py-name">nu_f</tt> <tt class="py-op">=</tt> <tt id="link-18" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-18', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-19" class="py-name" targets="Function dadi.Misc.ensure_1arg_func()=dadi.Misc-module.html#ensure_1arg_func"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-19', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">nu</tt><tt class="py-op">)</tt> </tt>
<a name="L165"></a><tt class="py-lineno">165</tt>  <tt class="py-line">    <tt class="py-name">gamma_f</tt> <tt class="py-op">=</tt> <tt id="link-20" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-20', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-21" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-21', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">gamma</tt><tt class="py-op">)</tt> </tt>
<a name="L166"></a><tt class="py-lineno">166</tt>  <tt class="py-line">    <tt class="py-name">h_f</tt> <tt class="py-op">=</tt> <tt id="link-22" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-22', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-23" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-23', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">h</tt><tt class="py-op">)</tt> </tt>
<a name="L167"></a><tt class="py-lineno">167</tt>  <tt class="py-line">    <tt class="py-name">theta0_f</tt> <tt class="py-op">=</tt> <tt id="link-24" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-24', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-25" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-25', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">theta0</tt><tt class="py-op">)</tt> </tt>
<a name="L168"></a><tt class="py-lineno">168</tt>  <tt class="py-line">    <tt class="py-name">beta_f</tt> <tt class="py-op">=</tt> <tt id="link-26" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-26', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-27" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-27', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
<a name="L169"></a><tt class="py-lineno">169</tt>  <tt class="py-line"> </tt>
<a name="L170"></a><tt class="py-lineno">170</tt>  <tt class="py-line">    <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">initial_t</tt> </tt>
<a name="L171"></a><tt class="py-lineno">171</tt>  <tt class="py-line">    <tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt> <tt class="py-op">=</tt> <tt class="py-name">nu_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">gamma_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">h_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L172"></a><tt class="py-lineno">172</tt>  <tt class="py-line">    <tt class="py-name">beta</tt> <tt class="py-op">=</tt> <tt class="py-name">beta_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L173"></a><tt class="py-lineno">173</tt>  <tt class="py-line">    <tt class="py-name">dx</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">)</tt> </tt>
<a name="L174"></a><tt class="py-lineno">174</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">current_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">T</tt><tt class="py-op">:</tt> </tt>
<a name="L175"></a><tt class="py-lineno">175</tt>  <tt class="py-line">        <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt id="link-28" class="py-name" targets="Function dadi.Integration._compute_dt()=dadi.Integration-module.html#_compute_dt"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-28', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma</tt><tt class="py-op">,</tt><tt class="py-name">h</tt><tt class="py-op">)</tt> </tt>
<a name="L176"></a><tt class="py-lineno">176</tt>  <tt class="py-line">        <tt class="py-name">this_dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt class="py-name">dt</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L177"></a><tt class="py-lineno">177</tt>  <tt class="py-line"> </tt>
<a name="L178"></a><tt class="py-lineno">178</tt>  <tt class="py-line">        <tt class="py-comment"># Because this is an implicit method, I need the *next* time's params.</tt> </tt>
<a name="L179"></a><tt class="py-lineno">179</tt>  <tt class="py-line">        <tt class="py-comment"># So there's a little inconsistency here, in that I'm estimating dt</tt> </tt>
<a name="L180"></a><tt class="py-lineno">180</tt>  <tt class="py-line">        <tt class="py-comment"># using the last timepoints nu,gamma,h.</tt> </tt>
<a name="L181"></a><tt class="py-lineno">181</tt>  <tt class="py-line">        <tt class="py-name">next_t</tt> <tt class="py-op">=</tt> <tt class="py-name">current_t</tt> <tt class="py-op">+</tt> <tt class="py-name">this_dt</tt> </tt>
<a name="L182"></a><tt class="py-lineno">182</tt>  <tt class="py-line">        <tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt> <tt class="py-op">=</tt> <tt class="py-name">nu_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">gamma_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">h_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L183"></a><tt class="py-lineno">183</tt>  <tt class="py-line">        <tt class="py-name">beta</tt> <tt class="py-op">=</tt> <tt class="py-name">beta_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L184"></a><tt class="py-lineno">184</tt>  <tt class="py-line">        <tt class="py-name">theta0</tt> <tt class="py-op">=</tt> <tt class="py-name">theta0_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L185"></a><tt class="py-lineno">185</tt>  <tt class="py-line"> </tt>
<a name="L186"></a><tt class="py-lineno">186</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">less</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">T</tt><tt class="py-op">,</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt><tt class="py-name">theta0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L187"></a><tt class="py-lineno">187</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A time, population size, migration rate, or '</tt> </tt>
<a name="L188"></a><tt class="py-lineno">188</tt>  <tt class="py-line">                             <tt class="py-string">'theta0 is &lt; 0. Has the model been mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L189"></a><tt class="py-lineno">189</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">equal</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">nu</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L190"></a><tt class="py-lineno">190</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A population size is 0. Has the model been '</tt> </tt>
<a name="L191"></a><tt class="py-lineno">191</tt>  <tt class="py-line">                             <tt class="py-string">'mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L192"></a><tt class="py-lineno">192</tt>  <tt class="py-line"> </tt>
<a name="L193"></a><tt class="py-lineno">193</tt>  <tt class="py-line">        <tt id="link-29" class="py-name" targets="Function dadi.Integration._inject_mutations_1D()=dadi.Integration-module.html#_inject_mutations_1D"><a title="dadi.Integration._inject_mutations_1D" class="py-name" href="#" onclick="return doclink('link-29', '_inject_mutations_1D', 'link-29');">_inject_mutations_1D</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">)</tt> </tt>
<a name="L194"></a><tt class="py-lineno">194</tt>  <tt class="py-line">        <tt class="py-comment"># Do each step in C, since it will be faster to compute the a,b,c</tt> </tt>
<a name="L195"></a><tt class="py-lineno">195</tt>  <tt class="py-line">        <tt class="py-comment"># matrices there.</tt> </tt>
<a name="L196"></a><tt class="py-lineno">196</tt>  <tt class="py-line">        <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-30" class="py-name" targets="Variable dadi.integration_c.implicit_1Dx=dadi.integration_c-module.html#implicit_1Dx"><a title="dadi.integration_c.implicit_1Dx" class="py-name" href="#" onclick="return doclink('link-30', 'implicit_1Dx', 'link-30');">implicit_1Dx</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt>  </tt>
<a name="L197"></a><tt class="py-lineno">197</tt>  <tt class="py-line">                                 <tt id="link-31" class="py-name"><a title="dadi.Integration.use_delj_trick" class="py-name" href="#" onclick="return doclink('link-31', 'use_delj_trick', 'link-1');">use_delj_trick</a></tt><tt class="py-op">=</tt><tt id="link-32" class="py-name"><a title="dadi.Integration.use_delj_trick" class="py-name" href="#" onclick="return doclink('link-32', 'use_delj_trick', 'link-1');">use_delj_trick</a></tt><tt class="py-op">)</tt> </tt>
<a name="L198"></a><tt class="py-lineno">198</tt>  <tt class="py-line">        <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">next_t</tt> </tt>
<a name="L199"></a><tt class="py-lineno">199</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="L200"></a><tt class="py-lineno">200</tt>  <tt class="py-line"> </tt>
<a name="two_pops"></a><div id="two_pops-def"><a name="L201"></a><tt class="py-lineno">201</tt> <a class="py-toggle" href="#" id="two_pops-toggle" onclick="return toggle('two_pops');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#two_pops">two_pops</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">T</tt><tt class="py-op">,</tt> <tt class="py-param">nu1</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">nu2</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">m12</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m21</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">gamma1</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">gamma2</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> </tt>
<a name="L202"></a><tt class="py-lineno">202</tt>  <tt class="py-line">             <tt class="py-param">h1</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">h2</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">initial_t</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">frozen1</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt>  </tt>
<a name="L203"></a><tt class="py-lineno">203</tt>  <tt class="py-line">             <tt class="py-param">frozen2</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="two_pops-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="two_pops-expanded"><a name="L204"></a><tt class="py-lineno">204</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L205"></a><tt class="py-lineno">205</tt>  <tt class="py-line"><tt class="py-docstring">    Integrate a 2-dimensional phi foward.</tt> </tt>
<a name="L206"></a><tt class="py-lineno">206</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L207"></a><tt class="py-lineno">207</tt>  <tt class="py-line"><tt class="py-docstring">    phi: Initial 2-dimensional phi</tt> </tt>
<a name="L208"></a><tt class="py-lineno">208</tt>  <tt class="py-line"><tt class="py-docstring">    xx: 1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed</tt> </tt>
<a name="L209"></a><tt class="py-lineno">209</tt>  <tt class="py-line"><tt class="py-docstring">        that this grid is used in all dimensions.</tt> </tt>
<a name="L210"></a><tt class="py-lineno">210</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L211"></a><tt class="py-lineno">211</tt>  <tt class="py-line"><tt class="py-docstring">    nu's, gamma's, m's, and theta0 may be functions of time.</tt> </tt>
<a name="L212"></a><tt class="py-lineno">212</tt>  <tt class="py-line"><tt class="py-docstring">    nu1,nu2: Population sizes</tt> </tt>
<a name="L213"></a><tt class="py-lineno">213</tt>  <tt class="py-line"><tt class="py-docstring">    gamma1,gamma2: Selection coefficients on *all* segregating alleles</tt> </tt>
<a name="L214"></a><tt class="py-lineno">214</tt>  <tt class="py-line"><tt class="py-docstring">    h1,h2: Dominance coefficients. h = 0.5 corresponds to genic selection.</tt> </tt>
<a name="L215"></a><tt class="py-lineno">215</tt>  <tt class="py-line"><tt class="py-docstring">    m12,m21: Migration rates. Note that m12 is the rate *into 1 from 2*.</tt> </tt>
<a name="L216"></a><tt class="py-lineno">216</tt>  <tt class="py-line"><tt class="py-docstring">    theta0: Propotional to ancestral size. Typically constant.</tt> </tt>
<a name="L217"></a><tt class="py-lineno">217</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L218"></a><tt class="py-lineno">218</tt>  <tt class="py-line"><tt class="py-docstring">    T: Time at which to halt integration</tt> </tt>
<a name="L219"></a><tt class="py-lineno">219</tt>  <tt class="py-line"><tt class="py-docstring">    initial_t: Time at which to start integration. (Note that this only matters</tt> </tt>
<a name="L220"></a><tt class="py-lineno">220</tt>  <tt class="py-line"><tt class="py-docstring">               if one of the demographic parameters is a function of time.)</tt> </tt>
<a name="L221"></a><tt class="py-lineno">221</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L222"></a><tt class="py-lineno">222</tt>  <tt class="py-line"><tt class="py-docstring">    Note: Generalizing to different grids in different phi directions is</tt> </tt>
<a name="L223"></a><tt class="py-lineno">223</tt>  <tt class="py-line"><tt class="py-docstring">          straightforward. The tricky part will be later doing the extrapolation</tt> </tt>
<a name="L224"></a><tt class="py-lineno">224</tt>  <tt class="py-line"><tt class="py-docstring">          correctly.</tt> </tt>
<a name="L225"></a><tt class="py-lineno">225</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L226"></a><tt class="py-lineno">226</tt>  <tt class="py-line">    <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L227"></a><tt class="py-lineno">227</tt>  <tt class="py-line"> </tt>
<a name="L228"></a><tt class="py-lineno">228</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">initial_t</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L229"></a><tt class="py-lineno">229</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
<a name="L230"></a><tt class="py-lineno">230</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">initial_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L231"></a><tt class="py-lineno">231</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'Final integration time T (%f) is less than '</tt> </tt>
<a name="L232"></a><tt class="py-lineno">232</tt>  <tt class="py-line">                         <tt class="py-string">'intial_time (%f). Integration cannot be run '</tt> </tt>
<a name="L233"></a><tt class="py-lineno">233</tt>  <tt class="py-line">                         <tt class="py-string">'backwards.'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">T</tt><tt class="py-op">,</tt> <tt class="py-name">initial_t</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L234"></a><tt class="py-lineno">234</tt>  <tt class="py-line"> </tt>
<a name="L235"></a><tt class="py-lineno">235</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-op">(</tt><tt class="py-name">frozen1</tt> <tt class="py-keyword">or</tt> <tt class="py-name">frozen2</tt><tt class="py-op">)</tt> <tt class="py-keyword">and</tt> <tt class="py-op">(</tt><tt class="py-name">m12</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m21</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L236"></a><tt class="py-lineno">236</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'Population cannot be frozen and have non-zero '</tt> </tt>
<a name="L237"></a><tt class="py-lineno">237</tt>  <tt class="py-line">                         <tt class="py-string">'migration to or from it.'</tt><tt class="py-op">)</tt> </tt>
<a name="L238"></a><tt class="py-lineno">238</tt>  <tt class="py-line"> </tt>
<a name="L239"></a><tt class="py-lineno">239</tt>  <tt class="py-line">    <tt class="py-name">vars_to_check</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt><tt class="py-op">,</tt><tt class="py-name">h1</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">,</tt><tt class="py-name">theta0</tt><tt class="py-op">]</tt> </tt>
<a name="L240"></a><tt class="py-lineno">240</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">all</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isscalar</tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">var</tt> <tt class="py-keyword">in</tt> <tt class="py-name">vars_to_check</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L241"></a><tt class="py-lineno">241</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-33" class="py-name" targets="Function dadi.Integration._two_pops_const_params()=dadi.Integration-module.html#_two_pops_const_params"><a title="dadi.Integration._two_pops_const_params" class="py-name" href="#" onclick="return doclink('link-33', '_two_pops_const_params', 'link-33');">_two_pops_const_params</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt><tt class="py-op">,</tt> <tt class="py-name">nu1</tt><tt class="py-op">,</tt> <tt class="py-name">nu2</tt><tt class="py-op">,</tt> <tt class="py-name">m12</tt><tt class="py-op">,</tt> <tt class="py-name">m21</tt><tt class="py-op">,</tt>  </tt>
<a name="L242"></a><tt class="py-lineno">242</tt>  <tt class="py-line">                                      <tt class="py-name">gamma1</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt><tt class="py-op">,</tt> <tt class="py-name">h2</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">,</tt> <tt class="py-name">initial_t</tt><tt class="py-op">,</tt> </tt>
<a name="L243"></a><tt class="py-lineno">243</tt>  <tt class="py-line">                                      <tt class="py-name">frozen1</tt><tt class="py-op">,</tt> <tt class="py-name">frozen2</tt><tt class="py-op">)</tt> </tt>
<a name="L244"></a><tt class="py-lineno">244</tt>  <tt class="py-line">    <tt class="py-name">yy</tt> <tt class="py-op">=</tt> <tt class="py-name">xx</tt> </tt>
<a name="L245"></a><tt class="py-lineno">245</tt>  <tt class="py-line"> </tt>
<a name="L246"></a><tt class="py-lineno">246</tt>  <tt class="py-line">    <tt class="py-name">nu1_f</tt> <tt class="py-op">=</tt> <tt id="link-34" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-34', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-35" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-35', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">nu1</tt><tt class="py-op">)</tt> </tt>
<a name="L247"></a><tt class="py-lineno">247</tt>  <tt class="py-line">    <tt class="py-name">nu2_f</tt> <tt class="py-op">=</tt> <tt id="link-36" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-36', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-37" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-37', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">nu2</tt><tt class="py-op">)</tt> </tt>
<a name="L248"></a><tt class="py-lineno">248</tt>  <tt class="py-line">    <tt class="py-name">m12_f</tt> <tt class="py-op">=</tt> <tt id="link-38" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-38', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-39" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-39', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">m12</tt><tt class="py-op">)</tt> </tt>
<a name="L249"></a><tt class="py-lineno">249</tt>  <tt class="py-line">    <tt class="py-name">m21_f</tt> <tt class="py-op">=</tt> <tt id="link-40" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-40', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-41" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-41', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">m21</tt><tt class="py-op">)</tt> </tt>
<a name="L250"></a><tt class="py-lineno">250</tt>  <tt class="py-line">    <tt class="py-name">gamma1_f</tt> <tt class="py-op">=</tt> <tt id="link-42" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-42', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-43" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-43', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">gamma1</tt><tt class="py-op">)</tt> </tt>
<a name="L251"></a><tt class="py-lineno">251</tt>  <tt class="py-line">    <tt class="py-name">gamma2_f</tt> <tt class="py-op">=</tt> <tt id="link-44" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-44', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-45" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-45', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">gamma2</tt><tt class="py-op">)</tt> </tt>
<a name="L252"></a><tt class="py-lineno">252</tt>  <tt class="py-line">    <tt class="py-name">h1_f</tt> <tt class="py-op">=</tt> <tt id="link-46" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-46', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-47" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-47', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">h1</tt><tt class="py-op">)</tt> </tt>
<a name="L253"></a><tt class="py-lineno">253</tt>  <tt class="py-line">    <tt class="py-name">h2_f</tt> <tt class="py-op">=</tt> <tt id="link-48" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-48', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-49" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-49', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">h2</tt><tt class="py-op">)</tt> </tt>
<a name="L254"></a><tt class="py-lineno">254</tt>  <tt class="py-line">    <tt class="py-name">theta0_f</tt> <tt class="py-op">=</tt> <tt id="link-50" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-50', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-51" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-51', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">theta0</tt><tt class="py-op">)</tt> </tt>
<a name="L255"></a><tt class="py-lineno">255</tt>  <tt class="py-line"> </tt>
<a name="L256"></a><tt class="py-lineno">256</tt>  <tt class="py-line">    <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">initial_t</tt> </tt>
<a name="L257"></a><tt class="py-lineno">257</tt>  <tt class="py-line">    <tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt> <tt class="py-op">=</tt> <tt class="py-name">nu1_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">nu2_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L258"></a><tt class="py-lineno">258</tt>  <tt class="py-line">    <tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m21</tt> <tt class="py-op">=</tt> <tt class="py-name">m12_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">m21_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L259"></a><tt class="py-lineno">259</tt>  <tt class="py-line">    <tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt> <tt class="py-op">=</tt> <tt class="py-name">gamma1_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L260"></a><tt class="py-lineno">260</tt>  <tt class="py-line">    <tt class="py-name">h1</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt> <tt class="py-op">=</tt> <tt class="py-name">h1_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">h2_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L261"></a><tt class="py-lineno">261</tt>  <tt class="py-line">    <tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">dy</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">)</tt><tt class="py-op">,</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">)</tt> </tt>
<a name="L262"></a><tt class="py-lineno">262</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">current_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">T</tt><tt class="py-op">:</tt> </tt>
<a name="L263"></a><tt class="py-lineno">263</tt>  <tt class="py-line">        <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt id="link-52" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-52', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m12</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">h1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> </tt>
<a name="L264"></a><tt class="py-lineno">264</tt>  <tt class="py-line">                 <tt id="link-53" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-53', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dy</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m21</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L265"></a><tt class="py-lineno">265</tt>  <tt class="py-line">        <tt class="py-name">this_dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt class="py-name">dt</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L266"></a><tt class="py-lineno">266</tt>  <tt class="py-line"> </tt>
<a name="L267"></a><tt class="py-lineno">267</tt>  <tt class="py-line">        <tt class="py-name">next_t</tt> <tt class="py-op">=</tt> <tt class="py-name">current_t</tt> <tt class="py-op">+</tt> <tt class="py-name">this_dt</tt> </tt>
<a name="L268"></a><tt class="py-lineno">268</tt>  <tt class="py-line"> </tt>
<a name="L269"></a><tt class="py-lineno">269</tt>  <tt class="py-line">        <tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt> <tt class="py-op">=</tt> <tt class="py-name">nu1_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">nu2_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L270"></a><tt class="py-lineno">270</tt>  <tt class="py-line">        <tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m21</tt> <tt class="py-op">=</tt> <tt class="py-name">m12_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">m21_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L271"></a><tt class="py-lineno">271</tt>  <tt class="py-line">        <tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt> <tt class="py-op">=</tt> <tt class="py-name">gamma1_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L272"></a><tt class="py-lineno">272</tt>  <tt class="py-line">        <tt class="py-name">h1</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt> <tt class="py-op">=</tt> <tt class="py-name">h1_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">h2_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L273"></a><tt class="py-lineno">273</tt>  <tt class="py-line">        <tt class="py-name">theta0</tt> <tt class="py-op">=</tt> <tt class="py-name">theta0_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L274"></a><tt class="py-lineno">274</tt>  <tt class="py-line"> </tt>
<a name="L275"></a><tt class="py-lineno">275</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">less</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">T</tt><tt class="py-op">,</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">theta0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L276"></a><tt class="py-lineno">276</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A time, population size, migration rate, or '</tt> </tt>
<a name="L277"></a><tt class="py-lineno">277</tt>  <tt class="py-line">                             <tt class="py-string">'theta0 is &lt; 0. Has the model been mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L278"></a><tt class="py-lineno">278</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">equal</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L279"></a><tt class="py-lineno">279</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A population size is 0. Has the model been '</tt> </tt>
<a name="L280"></a><tt class="py-lineno">280</tt>  <tt class="py-line">                             <tt class="py-string">'mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L281"></a><tt class="py-lineno">281</tt>  <tt class="py-line"> </tt>
<a name="L282"></a><tt class="py-lineno">282</tt>  <tt class="py-line">        <tt id="link-54" class="py-name" targets="Function dadi.Integration._inject_mutations_2D()=dadi.Integration-module.html#_inject_mutations_2D"><a title="dadi.Integration._inject_mutations_2D" class="py-name" href="#" onclick="return doclink('link-54', '_inject_mutations_2D', 'link-54');">_inject_mutations_2D</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">,</tt> <tt class="py-name">frozen1</tt><tt class="py-op">,</tt> <tt class="py-name">frozen2</tt><tt class="py-op">)</tt> </tt>
<a name="L283"></a><tt class="py-lineno">283</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen1</tt><tt class="py-op">:</tt>  </tt>
<a name="L284"></a><tt class="py-lineno">284</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-55" class="py-name" targets="Variable dadi.integration_c.implicit_2Dx=dadi.integration_c-module.html#implicit_2Dx"><a title="dadi.integration_c.implicit_2Dx" class="py-name" href="#" onclick="return doclink('link-55', 'implicit_2Dx', 'link-55');">implicit_2Dx</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">nu1</tt><tt class="py-op">,</tt> <tt class="py-name">m12</tt><tt class="py-op">,</tt> <tt class="py-name">gamma1</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt><tt class="py-op">,</tt> </tt>
<a name="L285"></a><tt class="py-lineno">285</tt>  <tt class="py-line">                                     <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt id="link-56" class="py-name"><a title="dadi.Integration.use_delj_trick" class="py-name" href="#" onclick="return doclink('link-56', 'use_delj_trick', 'link-1');">use_delj_trick</a></tt><tt class="py-op">)</tt> </tt>
<a name="L286"></a><tt class="py-lineno">286</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen2</tt><tt class="py-op">:</tt>  </tt>
<a name="L287"></a><tt class="py-lineno">287</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-57" class="py-name" targets="Variable dadi.integration_c.implicit_2Dy=dadi.integration_c-module.html#implicit_2Dy"><a title="dadi.integration_c.implicit_2Dy" class="py-name" href="#" onclick="return doclink('link-57', 'implicit_2Dy', 'link-57');">implicit_2Dy</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">nu2</tt><tt class="py-op">,</tt> <tt class="py-name">m21</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2</tt><tt class="py-op">,</tt> <tt class="py-name">h2</tt><tt class="py-op">,</tt> </tt>
<a name="L288"></a><tt class="py-lineno">288</tt>  <tt class="py-line">                                     <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt id="link-58" class="py-name"><a title="dadi.Integration.use_delj_trick" class="py-name" href="#" onclick="return doclink('link-58', 'use_delj_trick', 'link-1');">use_delj_trick</a></tt><tt class="py-op">)</tt> </tt>
<a name="L289"></a><tt class="py-lineno">289</tt>  <tt class="py-line"> </tt>
<a name="L290"></a><tt class="py-lineno">290</tt>  <tt class="py-line">        <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">next_t</tt> </tt>
<a name="L291"></a><tt class="py-lineno">291</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="L292"></a><tt class="py-lineno">292</tt>  <tt class="py-line"> </tt>
<a name="three_pops"></a><div id="three_pops-def"><a name="L293"></a><tt class="py-lineno">293</tt> <a class="py-toggle" href="#" id="three_pops-toggle" onclick="return toggle('three_pops');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#three_pops">three_pops</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">T</tt><tt class="py-op">,</tt> <tt class="py-param">nu1</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">nu2</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">nu3</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> </tt>
<a name="L294"></a><tt class="py-lineno">294</tt>  <tt class="py-line">               <tt class="py-param">m12</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m13</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m21</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m23</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m31</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m32</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> </tt>
<a name="L295"></a><tt class="py-lineno">295</tt>  <tt class="py-line">               <tt class="py-param">gamma1</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">gamma2</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">gamma3</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">h1</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">h2</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">h3</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> </tt>
<a name="L296"></a><tt class="py-lineno">296</tt>  <tt class="py-line">               <tt class="py-param">theta0</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">initial_t</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">frozen1</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> <tt class="py-param">frozen2</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> </tt>
<a name="L297"></a><tt class="py-lineno">297</tt>  <tt class="py-line">               <tt class="py-param">frozen3</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="three_pops-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="three_pops-expanded"><a name="L298"></a><tt class="py-lineno">298</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L299"></a><tt class="py-lineno">299</tt>  <tt class="py-line"><tt class="py-docstring">    Integrate a 3-dimensional phi foward.</tt> </tt>
<a name="L300"></a><tt class="py-lineno">300</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L301"></a><tt class="py-lineno">301</tt>  <tt class="py-line"><tt class="py-docstring">    phi: Initial 3-dimensional phi</tt> </tt>
<a name="L302"></a><tt class="py-lineno">302</tt>  <tt class="py-line"><tt class="py-docstring">    xx: 1-dimensional grid upon (0,1) overwhich phi is defined. It is assumed</tt> </tt>
<a name="L303"></a><tt class="py-lineno">303</tt>  <tt class="py-line"><tt class="py-docstring">        that this grid is used in all dimensions.</tt> </tt>
<a name="L304"></a><tt class="py-lineno">304</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L305"></a><tt class="py-lineno">305</tt>  <tt class="py-line"><tt class="py-docstring">    nu's, gamma's, m's, and theta0 may be functions of time.</tt> </tt>
<a name="L306"></a><tt class="py-lineno">306</tt>  <tt class="py-line"><tt class="py-docstring">    nu1,nu2,nu3: Population sizes</tt> </tt>
<a name="L307"></a><tt class="py-lineno">307</tt>  <tt class="py-line"><tt class="py-docstring">    gamma1,gamma2,gamma3: Selection coefficients on *all* segregating alleles</tt> </tt>
<a name="L308"></a><tt class="py-lineno">308</tt>  <tt class="py-line"><tt class="py-docstring">    h1,h2,h3: Dominance coefficients. h = 0.5 corresponds to genic selection.</tt> </tt>
<a name="L309"></a><tt class="py-lineno">309</tt>  <tt class="py-line"><tt class="py-docstring">    m12,m13,m21,m23,m31,m32: Migration rates. Note that m12 is the rate </tt> </tt>
<a name="L310"></a><tt class="py-lineno">310</tt>  <tt class="py-line"><tt class="py-docstring">                             *into 1 from 2*.</tt> </tt>
<a name="L311"></a><tt class="py-lineno">311</tt>  <tt class="py-line"><tt class="py-docstring">    theta0: Propotional to ancestral size. Typically constant.</tt> </tt>
<a name="L312"></a><tt class="py-lineno">312</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L313"></a><tt class="py-lineno">313</tt>  <tt class="py-line"><tt class="py-docstring">    T: Time at which to halt integration</tt> </tt>
<a name="L314"></a><tt class="py-lineno">314</tt>  <tt class="py-line"><tt class="py-docstring">    initial_t: Time at which to start integration. (Note that this only matters</tt> </tt>
<a name="L315"></a><tt class="py-lineno">315</tt>  <tt class="py-line"><tt class="py-docstring">               if one of the demographic parameters is a function of time.)</tt> </tt>
<a name="L316"></a><tt class="py-lineno">316</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L317"></a><tt class="py-lineno">317</tt>  <tt class="py-line"><tt class="py-docstring">    Note: Generalizing to different grids in different phi directions is</tt> </tt>
<a name="L318"></a><tt class="py-lineno">318</tt>  <tt class="py-line"><tt class="py-docstring">          straightforward. The tricky part will be later doing the extrapolation</tt> </tt>
<a name="L319"></a><tt class="py-lineno">319</tt>  <tt class="py-line"><tt class="py-docstring">          correctly.</tt> </tt>
<a name="L320"></a><tt class="py-lineno">320</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L321"></a><tt class="py-lineno">321</tt>  <tt class="py-line">    <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L322"></a><tt class="py-lineno">322</tt>  <tt class="py-line"> </tt>
<a name="L323"></a><tt class="py-lineno">323</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">initial_t</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L324"></a><tt class="py-lineno">324</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
<a name="L325"></a><tt class="py-lineno">325</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">initial_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L326"></a><tt class="py-lineno">326</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'Final integration time T (%f) is less than '</tt> </tt>
<a name="L327"></a><tt class="py-lineno">327</tt>  <tt class="py-line">                         <tt class="py-string">'intial_time (%f). Integration cannot be run '</tt> </tt>
<a name="L328"></a><tt class="py-lineno">328</tt>  <tt class="py-line">                         <tt class="py-string">'backwards.'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">T</tt><tt class="py-op">,</tt> <tt class="py-name">initial_t</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L329"></a><tt class="py-lineno">329</tt>  <tt class="py-line"> </tt>
<a name="L330"></a><tt class="py-lineno">330</tt>  <tt class="py-line"> </tt>
<a name="L331"></a><tt class="py-lineno">331</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-op">(</tt><tt class="py-name">frozen1</tt> <tt class="py-keyword">and</tt> <tt class="py-op">(</tt><tt class="py-name">m12</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m21</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m13</tt> <tt class="py-op">!=</tt><tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m31</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt>\ </tt>
<a name="L332"></a><tt class="py-lineno">332</tt>  <tt class="py-line">       <tt class="py-keyword">or</tt> <tt class="py-op">(</tt><tt class="py-name">frozen2</tt> <tt class="py-keyword">and</tt> <tt class="py-op">(</tt><tt class="py-name">m12</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m21</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m23</tt> <tt class="py-op">!=</tt><tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m32</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt>\ </tt>
<a name="L333"></a><tt class="py-lineno">333</tt>  <tt class="py-line">       <tt class="py-keyword">or</tt> <tt class="py-op">(</tt><tt class="py-name">frozen3</tt> <tt class="py-keyword">and</tt> <tt class="py-op">(</tt><tt class="py-name">m13</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m31</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m23</tt> <tt class="py-op">!=</tt><tt class="py-number">0</tt> <tt class="py-keyword">or</tt> <tt class="py-name">m32</tt> <tt class="py-op">!=</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L334"></a><tt class="py-lineno">334</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'Population cannot be frozen and have non-zero '</tt> </tt>
<a name="L335"></a><tt class="py-lineno">335</tt>  <tt class="py-line">                         <tt class="py-string">'migration to or from it.'</tt><tt class="py-op">)</tt> </tt>
<a name="L336"></a><tt class="py-lineno">336</tt>  <tt class="py-line"> </tt>
<a name="L337"></a><tt class="py-lineno">337</tt>  <tt class="py-line">    <tt class="py-name">vars_to_check</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt><tt class="py-op">,</tt><tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m13</tt><tt class="py-op">,</tt><tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">m23</tt><tt class="py-op">,</tt><tt class="py-name">m31</tt><tt class="py-op">,</tt><tt class="py-name">m32</tt><tt class="py-op">,</tt><tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt><tt class="py-op">,</tt> </tt>
<a name="L338"></a><tt class="py-lineno">338</tt>  <tt class="py-line">                     <tt class="py-name">gamma3</tt><tt class="py-op">,</tt><tt class="py-name">h1</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">,</tt><tt class="py-name">h3</tt><tt class="py-op">,</tt><tt class="py-name">theta0</tt><tt class="py-op">]</tt> </tt>
<a name="L339"></a><tt class="py-lineno">339</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">all</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isscalar</tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">var</tt> <tt class="py-keyword">in</tt> <tt class="py-name">vars_to_check</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L340"></a><tt class="py-lineno">340</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-59" class="py-name" targets="Function dadi.Integration._three_pops_const_params()=dadi.Integration-module.html#_three_pops_const_params"><a title="dadi.Integration._three_pops_const_params" class="py-name" href="#" onclick="return doclink('link-59', '_three_pops_const_params', 'link-59');">_three_pops_const_params</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt><tt class="py-op">,</tt> <tt class="py-name">nu1</tt><tt class="py-op">,</tt> <tt class="py-name">nu2</tt><tt class="py-op">,</tt> <tt class="py-name">nu3</tt><tt class="py-op">,</tt>  </tt>
<a name="L341"></a><tt class="py-lineno">341</tt>  <tt class="py-line">                                        <tt class="py-name">m12</tt><tt class="py-op">,</tt> <tt class="py-name">m13</tt><tt class="py-op">,</tt> <tt class="py-name">m21</tt><tt class="py-op">,</tt> <tt class="py-name">m23</tt><tt class="py-op">,</tt> <tt class="py-name">m31</tt><tt class="py-op">,</tt> <tt class="py-name">m32</tt><tt class="py-op">,</tt>  </tt>
<a name="L342"></a><tt class="py-lineno">342</tt>  <tt class="py-line">                                        <tt class="py-name">gamma1</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2</tt><tt class="py-op">,</tt> <tt class="py-name">gamma3</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt><tt class="py-op">,</tt> <tt class="py-name">h2</tt><tt class="py-op">,</tt> <tt class="py-name">h3</tt><tt class="py-op">,</tt> </tt>
<a name="L343"></a><tt class="py-lineno">343</tt>  <tt class="py-line">                                        <tt class="py-name">theta0</tt><tt class="py-op">,</tt> <tt class="py-name">initial_t</tt><tt class="py-op">)</tt> </tt>
<a name="L344"></a><tt class="py-lineno">344</tt>  <tt class="py-line">    <tt class="py-name">zz</tt> <tt class="py-op">=</tt> <tt class="py-name">yy</tt> <tt class="py-op">=</tt> <tt class="py-name">xx</tt> </tt>
<a name="L345"></a><tt class="py-lineno">345</tt>  <tt class="py-line"> </tt>
<a name="L346"></a><tt class="py-lineno">346</tt>  <tt class="py-line">    <tt class="py-name">nu1_f</tt> <tt class="py-op">=</tt> <tt id="link-60" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-60', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-61" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-61', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">nu1</tt><tt class="py-op">)</tt> </tt>
<a name="L347"></a><tt class="py-lineno">347</tt>  <tt class="py-line">    <tt class="py-name">nu2_f</tt> <tt class="py-op">=</tt> <tt id="link-62" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-62', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-63" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-63', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">nu2</tt><tt class="py-op">)</tt> </tt>
<a name="L348"></a><tt class="py-lineno">348</tt>  <tt class="py-line">    <tt class="py-name">nu3_f</tt> <tt class="py-op">=</tt> <tt id="link-64" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-64', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-65" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-65', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">nu3</tt><tt class="py-op">)</tt> </tt>
<a name="L349"></a><tt class="py-lineno">349</tt>  <tt class="py-line">    <tt class="py-name">m12_f</tt> <tt class="py-op">=</tt> <tt id="link-66" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-66', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-67" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-67', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">m12</tt><tt class="py-op">)</tt> </tt>
<a name="L350"></a><tt class="py-lineno">350</tt>  <tt class="py-line">    <tt class="py-name">m13_f</tt> <tt class="py-op">=</tt> <tt id="link-68" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-68', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-69" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-69', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">m13</tt><tt class="py-op">)</tt> </tt>
<a name="L351"></a><tt class="py-lineno">351</tt>  <tt class="py-line">    <tt class="py-name">m21_f</tt> <tt class="py-op">=</tt> <tt id="link-70" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-70', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-71" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-71', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">m21</tt><tt class="py-op">)</tt> </tt>
<a name="L352"></a><tt class="py-lineno">352</tt>  <tt class="py-line">    <tt class="py-name">m23_f</tt> <tt class="py-op">=</tt> <tt id="link-72" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-72', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-73" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-73', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">m23</tt><tt class="py-op">)</tt> </tt>
<a name="L353"></a><tt class="py-lineno">353</tt>  <tt class="py-line">    <tt class="py-name">m31_f</tt> <tt class="py-op">=</tt> <tt id="link-74" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-74', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-75" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-75', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">m31</tt><tt class="py-op">)</tt> </tt>
<a name="L354"></a><tt class="py-lineno">354</tt>  <tt class="py-line">    <tt class="py-name">m32_f</tt> <tt class="py-op">=</tt> <tt id="link-76" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-76', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-77" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-77', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">m32</tt><tt class="py-op">)</tt> </tt>
<a name="L355"></a><tt class="py-lineno">355</tt>  <tt class="py-line">    <tt class="py-name">gamma1_f</tt> <tt class="py-op">=</tt> <tt id="link-78" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-78', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-79" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-79', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">gamma1</tt><tt class="py-op">)</tt> </tt>
<a name="L356"></a><tt class="py-lineno">356</tt>  <tt class="py-line">    <tt class="py-name">gamma2_f</tt> <tt class="py-op">=</tt> <tt id="link-80" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-80', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-81" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-81', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">gamma2</tt><tt class="py-op">)</tt> </tt>
<a name="L357"></a><tt class="py-lineno">357</tt>  <tt class="py-line">    <tt class="py-name">gamma3_f</tt> <tt class="py-op">=</tt> <tt id="link-82" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-82', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-83" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-83', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">gamma3</tt><tt class="py-op">)</tt> </tt>
<a name="L358"></a><tt class="py-lineno">358</tt>  <tt class="py-line">    <tt class="py-name">h1_f</tt> <tt class="py-op">=</tt> <tt id="link-84" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-84', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-85" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-85', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">h1</tt><tt class="py-op">)</tt> </tt>
<a name="L359"></a><tt class="py-lineno">359</tt>  <tt class="py-line">    <tt class="py-name">h2_f</tt> <tt class="py-op">=</tt> <tt id="link-86" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-86', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-87" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-87', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">h2</tt><tt class="py-op">)</tt> </tt>
<a name="L360"></a><tt class="py-lineno">360</tt>  <tt class="py-line">    <tt class="py-name">h3_f</tt> <tt class="py-op">=</tt> <tt id="link-88" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-88', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-89" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-89', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">h3</tt><tt class="py-op">)</tt> </tt>
<a name="L361"></a><tt class="py-lineno">361</tt>  <tt class="py-line">    <tt class="py-name">theta0_f</tt> <tt class="py-op">=</tt> <tt id="link-90" class="py-name"><a title="dadi.Misc" class="py-name" href="#" onclick="return doclink('link-90', 'Misc', 'link-2');">Misc</a></tt><tt class="py-op">.</tt><tt id="link-91" class="py-name"><a title="dadi.Misc.ensure_1arg_func" class="py-name" href="#" onclick="return doclink('link-91', 'ensure_1arg_func', 'link-19');">ensure_1arg_func</a></tt><tt class="py-op">(</tt><tt class="py-name">theta0</tt><tt class="py-op">)</tt> </tt>
<a name="L362"></a><tt class="py-lineno">362</tt>  <tt class="py-line"> </tt>
<a name="L363"></a><tt class="py-lineno">363</tt>  <tt class="py-line">    <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">initial_t</tt> </tt>
<a name="L364"></a><tt class="py-lineno">364</tt>  <tt class="py-line">    <tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt> <tt class="py-op">=</tt> <tt class="py-name">nu1_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">nu2_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">nu3_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L365"></a><tt class="py-lineno">365</tt>  <tt class="py-line">    <tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m13</tt> <tt class="py-op">=</tt> <tt class="py-name">m12_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">m13_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L366"></a><tt class="py-lineno">366</tt>  <tt class="py-line">    <tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">m23</tt> <tt class="py-op">=</tt> <tt class="py-name">m21_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">m23_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L367"></a><tt class="py-lineno">367</tt>  <tt class="py-line">    <tt class="py-name">m31</tt><tt class="py-op">,</tt><tt class="py-name">m32</tt> <tt class="py-op">=</tt> <tt class="py-name">m31_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">m32_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L368"></a><tt class="py-lineno">368</tt>  <tt class="py-line">    <tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt> <tt class="py-op">=</tt> <tt class="py-name">gamma1_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L369"></a><tt class="py-lineno">369</tt>  <tt class="py-line">    <tt class="py-name">gamma3</tt> <tt class="py-op">=</tt> <tt class="py-name">gamma3_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L370"></a><tt class="py-lineno">370</tt>  <tt class="py-line">    <tt class="py-name">h1</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">,</tt><tt class="py-name">h3</tt> <tt class="py-op">=</tt> <tt class="py-name">h1_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">h2_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">h3_f</tt><tt class="py-op">(</tt><tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L371"></a><tt class="py-lineno">371</tt>  <tt class="py-line">    <tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">dy</tt><tt class="py-op">,</tt><tt class="py-name">dz</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">)</tt><tt class="py-op">,</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">)</tt><tt class="py-op">,</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">zz</tt><tt class="py-op">)</tt> </tt>
<a name="L372"></a><tt class="py-lineno">372</tt>  <tt class="py-line">    <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt id="link-92" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-92', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m13</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">h1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> </tt>
<a name="L373"></a><tt class="py-lineno">373</tt>  <tt class="py-line">             <tt id="link-93" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-93', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dy</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">m23</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> </tt>
<a name="L374"></a><tt class="py-lineno">374</tt>  <tt class="py-line">             <tt id="link-94" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-94', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dz</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m31</tt><tt class="py-op">,</tt><tt class="py-name">m32</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma3</tt><tt class="py-op">,</tt><tt class="py-name">h3</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L375"></a><tt class="py-lineno">375</tt>  <tt class="py-line">    <tt class="py-name">steps</tt> <tt class="py-op">=</tt> <tt class="py-number">0</tt> </tt>
<a name="L376"></a><tt class="py-lineno">376</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">current_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">T</tt><tt class="py-op">:</tt> </tt>
<a name="L377"></a><tt class="py-lineno">377</tt>  <tt class="py-line">        <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt id="link-95" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-95', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m13</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">h1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> </tt>
<a name="L378"></a><tt class="py-lineno">378</tt>  <tt class="py-line">                 <tt id="link-96" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-96', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dy</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">m23</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> </tt>
<a name="L379"></a><tt class="py-lineno">379</tt>  <tt class="py-line">                 <tt id="link-97" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-97', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dz</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m31</tt><tt class="py-op">,</tt><tt class="py-name">m32</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma3</tt><tt class="py-op">,</tt><tt class="py-name">h3</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L380"></a><tt class="py-lineno">380</tt>  <tt class="py-line">        <tt class="py-name">this_dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt class="py-name">dt</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L381"></a><tt class="py-lineno">381</tt>  <tt class="py-line"> </tt>
<a name="L382"></a><tt class="py-lineno">382</tt>  <tt class="py-line">        <tt class="py-name">next_t</tt> <tt class="py-op">=</tt> <tt class="py-name">current_t</tt> <tt class="py-op">+</tt> <tt class="py-name">this_dt</tt> </tt>
<a name="L383"></a><tt class="py-lineno">383</tt>  <tt class="py-line">        <tt class="py-name">steps</tt> <tt class="py-op">+=</tt> <tt class="py-number">1</tt> </tt>
<a name="L384"></a><tt class="py-lineno">384</tt>  <tt class="py-line"> </tt>
<a name="L385"></a><tt class="py-lineno">385</tt>  <tt class="py-line">        <tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt> <tt class="py-op">=</tt> <tt class="py-name">nu1_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">nu2_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">nu3_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L386"></a><tt class="py-lineno">386</tt>  <tt class="py-line">        <tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m13</tt> <tt class="py-op">=</tt> <tt class="py-name">m12_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">m13_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L387"></a><tt class="py-lineno">387</tt>  <tt class="py-line">        <tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">m23</tt> <tt class="py-op">=</tt> <tt class="py-name">m21_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">m23_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L388"></a><tt class="py-lineno">388</tt>  <tt class="py-line">        <tt class="py-name">m31</tt><tt class="py-op">,</tt><tt class="py-name">m32</tt> <tt class="py-op">=</tt> <tt class="py-name">m31_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">m32_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L389"></a><tt class="py-lineno">389</tt>  <tt class="py-line">        <tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt> <tt class="py-op">=</tt> <tt class="py-name">gamma1_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L390"></a><tt class="py-lineno">390</tt>  <tt class="py-line">        <tt class="py-name">gamma3</tt> <tt class="py-op">=</tt> <tt class="py-name">gamma3_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L391"></a><tt class="py-lineno">391</tt>  <tt class="py-line">        <tt class="py-name">h1</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">,</tt><tt class="py-name">h3</tt> <tt class="py-op">=</tt> <tt class="py-name">h1_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">h2_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-name">h3_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L392"></a><tt class="py-lineno">392</tt>  <tt class="py-line">        <tt class="py-name">theta0</tt> <tt class="py-op">=</tt> <tt class="py-name">theta0_f</tt><tt class="py-op">(</tt><tt class="py-name">next_t</tt><tt class="py-op">)</tt> </tt>
<a name="L393"></a><tt class="py-lineno">393</tt>  <tt class="py-line"> </tt>
<a name="L394"></a><tt class="py-lineno">394</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">less</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">T</tt><tt class="py-op">,</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt><tt class="py-op">,</tt><tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m13</tt><tt class="py-op">,</tt><tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">m23</tt><tt class="py-op">,</tt><tt class="py-name">m31</tt><tt class="py-op">,</tt><tt class="py-name">m32</tt><tt class="py-op">,</tt><tt class="py-name">theta0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> </tt>
<a name="L395"></a><tt class="py-lineno">395</tt>  <tt class="py-line">                                <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L396"></a><tt class="py-lineno">396</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A time, population size, migration rate, or '</tt> </tt>
<a name="L397"></a><tt class="py-lineno">397</tt>  <tt class="py-line">                             <tt class="py-string">'theta0 is &lt; 0. Has the model been mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L398"></a><tt class="py-lineno">398</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">equal</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L399"></a><tt class="py-lineno">399</tt>  <tt class="py-line">            <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A population size is 0. Has the model been '</tt> </tt>
<a name="L400"></a><tt class="py-lineno">400</tt>  <tt class="py-line">                             <tt class="py-string">'mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L401"></a><tt class="py-lineno">401</tt>  <tt class="py-line"> </tt>
<a name="L402"></a><tt class="py-lineno">402</tt>  <tt class="py-line">        <tt id="link-98" class="py-name" targets="Function dadi.Integration._inject_mutations_3D()=dadi.Integration-module.html#_inject_mutations_3D"><a title="dadi.Integration._inject_mutations_3D" class="py-name" href="#" onclick="return doclink('link-98', '_inject_mutations_3D', 'link-98');">_inject_mutations_3D</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">zz</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">,</tt> </tt>
<a name="L403"></a><tt class="py-lineno">403</tt>  <tt class="py-line">                             <tt class="py-name">frozen1</tt><tt class="py-op">,</tt> <tt class="py-name">frozen2</tt><tt class="py-op">,</tt> <tt class="py-name">frozen3</tt><tt class="py-op">)</tt> </tt>
<a name="L404"></a><tt class="py-lineno">404</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen1</tt><tt class="py-op">:</tt> </tt>
<a name="L405"></a><tt class="py-lineno">405</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-99" class="py-name" targets="Variable dadi.integration_c.implicit_3Dx=dadi.integration_c-module.html#implicit_3Dx"><a title="dadi.integration_c.implicit_3Dx" class="py-name" href="#" onclick="return doclink('link-99', 'implicit_3Dx', 'link-99');">implicit_3Dx</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">zz</tt><tt class="py-op">,</tt> <tt class="py-name">nu1</tt><tt class="py-op">,</tt> <tt class="py-name">m12</tt><tt class="py-op">,</tt> <tt class="py-name">m13</tt><tt class="py-op">,</tt>  </tt>
<a name="L406"></a><tt class="py-lineno">406</tt>  <tt class="py-line">                                     <tt class="py-name">gamma1</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt id="link-100" class="py-name"><a title="dadi.Integration.use_delj_trick" class="py-name" href="#" onclick="return doclink('link-100', 'use_delj_trick', 'link-1');">use_delj_trick</a></tt><tt class="py-op">)</tt> </tt>
<a name="L407"></a><tt class="py-lineno">407</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen2</tt><tt class="py-op">:</tt> </tt>
<a name="L408"></a><tt class="py-lineno">408</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-101" class="py-name" targets="Variable dadi.integration_c.implicit_3Dy=dadi.integration_c-module.html#implicit_3Dy"><a title="dadi.integration_c.implicit_3Dy" class="py-name" href="#" onclick="return doclink('link-101', 'implicit_3Dy', 'link-101');">implicit_3Dy</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">zz</tt><tt class="py-op">,</tt> <tt class="py-name">nu2</tt><tt class="py-op">,</tt> <tt class="py-name">m21</tt><tt class="py-op">,</tt> <tt class="py-name">m23</tt><tt class="py-op">,</tt>  </tt>
<a name="L409"></a><tt class="py-lineno">409</tt>  <tt class="py-line">                                     <tt class="py-name">gamma2</tt><tt class="py-op">,</tt> <tt class="py-name">h2</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt id="link-102" class="py-name"><a title="dadi.Integration.use_delj_trick" class="py-name" href="#" onclick="return doclink('link-102', 'use_delj_trick', 'link-1');">use_delj_trick</a></tt><tt class="py-op">)</tt> </tt>
<a name="L410"></a><tt class="py-lineno">410</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen3</tt><tt class="py-op">:</tt> </tt>
<a name="L411"></a><tt class="py-lineno">411</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-103" class="py-name" targets="Variable dadi.integration_c.implicit_3Dz=dadi.integration_c-module.html#implicit_3Dz"><a title="dadi.integration_c.implicit_3Dz" class="py-name" href="#" onclick="return doclink('link-103', 'implicit_3Dz', 'link-103');">implicit_3Dz</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">zz</tt><tt class="py-op">,</tt> <tt class="py-name">nu3</tt><tt class="py-op">,</tt> <tt class="py-name">m31</tt><tt class="py-op">,</tt> <tt class="py-name">m32</tt><tt class="py-op">,</tt>  </tt>
<a name="L412"></a><tt class="py-lineno">412</tt>  <tt class="py-line">                                     <tt class="py-name">gamma3</tt><tt class="py-op">,</tt> <tt class="py-name">h3</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt id="link-104" class="py-name"><a title="dadi.Integration.use_delj_trick" class="py-name" href="#" onclick="return doclink('link-104', 'use_delj_trick', 'link-1');">use_delj_trick</a></tt><tt class="py-op">)</tt> </tt>
<a name="L413"></a><tt class="py-lineno">413</tt>  <tt class="py-line"> </tt>
<a name="L414"></a><tt class="py-lineno">414</tt>  <tt class="py-line">        <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">next_t</tt> </tt>
<a name="L415"></a><tt class="py-lineno">415</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="L416"></a><tt class="py-lineno">416</tt>  <tt class="py-line"> </tt>
<a name="L417"></a><tt class="py-lineno">417</tt>  <tt class="py-line"><tt class="py-comment">#</tt> </tt>
<a name="L418"></a><tt class="py-lineno">418</tt>  <tt class="py-line"><tt class="py-comment"># Here are the python versions of the population genetic functions.</tt> </tt>
<a name="L419"></a><tt class="py-lineno">419</tt>  <tt class="py-line"><tt class="py-comment">#</tt> </tt>
<a name="_Vfunc"></a><div id="_Vfunc-def"><a name="L420"></a><tt class="py-lineno">420</tt> <a class="py-toggle" href="#" id="_Vfunc-toggle" onclick="return toggle('_Vfunc');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_Vfunc">_Vfunc</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">nu</tt><tt class="py-op">,</tt> <tt class="py-param">beta</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Vfunc-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_Vfunc-expanded"><a name="L421"></a><tt class="py-lineno">421</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-number">1.</tt><tt class="py-op">/</tt><tt class="py-name">nu</tt> <tt class="py-op">*</tt> <tt class="py-name">x</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">beta</tt><tt class="py-op">+</tt><tt class="py-number">1.</tt><tt class="py-op">)</tt><tt class="py-op">**</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">4.</tt><tt class="py-op">*</tt><tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
</div><a name="_Mfunc1D"></a><div id="_Mfunc1D-def"><a name="L422"></a><tt class="py-lineno">422</tt> <a class="py-toggle" href="#" id="_Mfunc1D-toggle" onclick="return toggle('_Mfunc1D');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_Mfunc1D">_Mfunc1D</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">gamma</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Mfunc1D-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_Mfunc1D-expanded"><a name="L423"></a><tt class="py-lineno">423</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">gamma</tt> <tt class="py-op">*</tt> <tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-name">h</tt> <tt class="py-op">+</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">h</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">x</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
</div><a name="_Mfunc2D"></a><div id="_Mfunc2D-def"><a name="L424"></a><tt class="py-lineno">424</tt> <a class="py-toggle" href="#" id="_Mfunc2D-toggle" onclick="return toggle('_Mfunc2D');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_Mfunc2D">_Mfunc2D</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">,</tt><tt class="py-param">y</tt><tt class="py-op">,</tt> <tt class="py-param">mxy</tt><tt class="py-op">,</tt> <tt class="py-param">gamma</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Mfunc2D-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_Mfunc2D-expanded"><a name="L425"></a><tt class="py-lineno">425</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">mxy</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">y</tt><tt class="py-op">-</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">gamma</tt> <tt class="py-op">*</tt> <tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-name">h</tt> <tt class="py-op">+</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">h</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">x</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
</div><a name="_Mfunc3D"></a><div id="_Mfunc3D-def"><a name="L426"></a><tt class="py-lineno">426</tt> <a class="py-toggle" href="#" id="_Mfunc3D-toggle" onclick="return toggle('_Mfunc3D');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_Mfunc3D">_Mfunc3D</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">,</tt><tt class="py-param">y</tt><tt class="py-op">,</tt><tt class="py-param">z</tt><tt class="py-op">,</tt> <tt class="py-param">mxy</tt><tt class="py-op">,</tt><tt class="py-param">mxz</tt><tt class="py-op">,</tt> <tt class="py-param">gamma</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Mfunc3D-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_Mfunc3D-expanded"><a name="L427"></a><tt class="py-lineno">427</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">mxy</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">y</tt><tt class="py-op">-</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">mxz</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-name">z</tt><tt class="py-op">-</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">gamma</tt> <tt class="py-op">*</tt> <tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-name">h</tt> <tt class="py-op">+</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">h</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">x</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
</div><a name="L428"></a><tt class="py-lineno">428</tt>  <tt class="py-line"> </tt>
<a name="_compute_dfactor"></a><div id="_compute_dfactor-def"><a name="L429"></a><tt class="py-lineno">429</tt> <a class="py-toggle" href="#" id="_compute_dfactor-toggle" onclick="return toggle('_compute_dfactor');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_compute_dfactor">_compute_dfactor</a><tt class="py-op">(</tt><tt class="py-param">dx</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_compute_dfactor-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_compute_dfactor-expanded"><a name="L430"></a><tt class="py-lineno">430</tt>  <tt class="py-line">    <tt class="py-docstring">r"""</tt> </tt>
<a name="L431"></a><tt class="py-lineno">431</tt>  <tt class="py-line"><tt class="py-docstring">    \Delta_j from the paper.</tt> </tt>
<a name="L432"></a><tt class="py-lineno">432</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L433"></a><tt class="py-lineno">433</tt>  <tt class="py-line">    <tt class="py-comment"># Controls how we take the derivative of the flux. The values here depend</tt> </tt>
<a name="L434"></a><tt class="py-lineno">434</tt>  <tt class="py-line">    <tt class="py-comment">#  on the fact that we're defining our probability integral using the</tt> </tt>
<a name="L435"></a><tt class="py-lineno">435</tt>  <tt class="py-line">    <tt class="py-comment">#  trapezoid rule.</tt> </tt>
<a name="L436"></a><tt class="py-lineno">436</tt>  <tt class="py-line">    <tt class="py-name">dfactor</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">len</tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt><tt class="py-op">+</tt><tt class="py-number">1</tt><tt class="py-op">)</tt> </tt>
<a name="L437"></a><tt class="py-lineno">437</tt>  <tt class="py-line">    <tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L438"></a><tt class="py-lineno">438</tt>  <tt class="py-line">    <tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L439"></a><tt class="py-lineno">439</tt>  <tt class="py-line">    <tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L440"></a><tt class="py-lineno">440</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">dfactor</tt> </tt>
</div><a name="L441"></a><tt class="py-lineno">441</tt>  <tt class="py-line"> </tt>
<a name="_compute_delj"></a><div id="_compute_delj-def"><a name="L442"></a><tt class="py-lineno">442</tt> <a class="py-toggle" href="#" id="_compute_delj-toggle" onclick="return toggle('_compute_delj');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_compute_delj">_compute_delj</a><tt class="py-op">(</tt><tt class="py-param">dx</tt><tt class="py-op">,</tt> <tt class="py-param">MInt</tt><tt class="py-op">,</tt> <tt class="py-param">VInt</tt><tt class="py-op">,</tt> <tt class="py-param">axis</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_compute_delj-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_compute_delj-expanded"><a name="L443"></a><tt class="py-lineno">443</tt>  <tt class="py-line">    <tt class="py-docstring">r"""</tt> </tt>
<a name="L444"></a><tt class="py-lineno">444</tt>  <tt class="py-line"><tt class="py-docstring">    Chang an Cooper's \delta_j term. Typically we set this to 0.5.</tt> </tt>
<a name="L445"></a><tt class="py-lineno">445</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L446"></a><tt class="py-lineno">446</tt>  <tt class="py-line">    <tt class="py-comment"># Chang and Cooper's fancy delta j trick...</tt> </tt>
<a name="L447"></a><tt class="py-lineno">447</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt id="link-105" class="py-name"><a title="dadi.Integration.use_delj_trick" class="py-name" href="#" onclick="return doclink('link-105', 'use_delj_trick', 'link-1');">use_delj_trick</a></tt><tt class="py-op">:</tt> </tt>
<a name="L448"></a><tt class="py-lineno">448</tt>  <tt class="py-line">        <tt class="py-comment"># upslice will raise the dimensionality of dx and VInt to be appropriate</tt> </tt>
<a name="L449"></a><tt class="py-lineno">449</tt>  <tt class="py-line">        <tt class="py-comment"># for functioning with MInt.</tt> </tt>
<a name="L450"></a><tt class="py-lineno">450</tt>  <tt class="py-line">        <tt class="py-name">upslice</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">nuax</tt> <tt class="py-keyword">for</tt> <tt class="py-name">ii</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-name">MInt</tt><tt class="py-op">.</tt><tt class="py-name">ndim</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L451"></a><tt class="py-lineno">451</tt>  <tt class="py-line">        <tt class="py-name">upslice</tt> <tt class="py-op">[</tt><tt class="py-name">axis</tt><tt class="py-op">]</tt> <tt class="py-op">=</tt> <tt class="py-name">slice</tt><tt class="py-op">(</tt><tt class="py-name">None</tt><tt class="py-op">)</tt> </tt>
<a name="L452"></a><tt class="py-lineno">452</tt>  <tt class="py-line"> </tt>
<a name="L453"></a><tt class="py-lineno">453</tt>  <tt class="py-line">        <tt class="py-name">wj</tt> <tt class="py-op">=</tt> <tt class="py-number">2</tt> <tt class="py-op">*</tt><tt class="py-name">MInt</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-name">upslice</tt><tt class="py-op">]</tt> </tt>
<a name="L454"></a><tt class="py-lineno">454</tt>  <tt class="py-line">        <tt class="py-name">epsj</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">exp</tt><tt class="py-op">(</tt><tt class="py-name">wj</tt><tt class="py-op">/</tt><tt class="py-name">VInt</tt><tt class="py-op">[</tt><tt class="py-name">upslice</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L455"></a><tt class="py-lineno">455</tt>  <tt class="py-line">        <tt class="py-name">delj</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">epsj</tt><tt class="py-op">*</tt><tt class="py-name">wj</tt> <tt class="py-op">+</tt> <tt class="py-name">epsj</tt> <tt class="py-op">*</tt> <tt class="py-name">VInt</tt><tt class="py-op">[</tt><tt class="py-name">upslice</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">VInt</tt><tt class="py-op">[</tt><tt class="py-name">upslice</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-name">wj</tt> <tt class="py-op">-</tt> <tt class="py-name">epsj</tt><tt class="py-op">*</tt><tt class="py-name">wj</tt><tt class="py-op">)</tt> </tt>
<a name="L456"></a><tt class="py-lineno">456</tt>  <tt class="py-line">        <tt class="py-comment"># These where statements filter out edge case for delj</tt> </tt>
<a name="L457"></a><tt class="py-lineno">457</tt>  <tt class="py-line">        <tt class="py-name">delj</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">where</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isnan</tt><tt class="py-op">(</tt><tt class="py-name">delj</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-name">delj</tt><tt class="py-op">)</tt> </tt>
<a name="L458"></a><tt class="py-lineno">458</tt>  <tt class="py-line">        <tt class="py-name">delj</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">where</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isinf</tt><tt class="py-op">(</tt><tt class="py-name">delj</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> <tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-name">delj</tt><tt class="py-op">)</tt> </tt>
<a name="L459"></a><tt class="py-lineno">459</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L460"></a><tt class="py-lineno">460</tt>  <tt class="py-line">        <tt class="py-name">delj</tt> <tt class="py-op">=</tt> <tt class="py-number">0.5</tt> </tt>
<a name="L461"></a><tt class="py-lineno">461</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">delj</tt> </tt>
</div><a name="L462"></a><tt class="py-lineno">462</tt>  <tt class="py-line"> </tt>
<a name="_one_pop_const_params"></a><div id="_one_pop_const_params-def"><a name="L463"></a><tt class="py-lineno">463</tt> <a class="py-toggle" href="#" id="_one_pop_const_params-toggle" onclick="return toggle('_one_pop_const_params');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_one_pop_const_params">_one_pop_const_params</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">T</tt><tt class="py-op">,</tt> <tt class="py-param">nu</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">gamma</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt>  </tt>
<a name="L464"></a><tt class="py-lineno">464</tt>  <tt class="py-line">                          <tt class="py-param">initial_t</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">beta</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_one_pop_const_params-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_one_pop_const_params-expanded"><a name="L465"></a><tt class="py-lineno">465</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L466"></a><tt class="py-lineno">466</tt>  <tt class="py-line"><tt class="py-docstring">    Integrate one population with constant parameters.</tt> </tt>
<a name="L467"></a><tt class="py-lineno">467</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L468"></a><tt class="py-lineno">468</tt>  <tt class="py-line"><tt class="py-docstring">    In this case, we can precompute our a,b,c matrices for the linear system</tt> </tt>
<a name="L469"></a><tt class="py-lineno">469</tt>  <tt class="py-line"><tt class="py-docstring">    we need to evolve. This we can efficiently do in Python, rather than </tt> </tt>
<a name="L470"></a><tt class="py-lineno">470</tt>  <tt class="py-line"><tt class="py-docstring">    relying on C. The nice thing is that the Python is much faster to debug.</tt> </tt>
<a name="L471"></a><tt class="py-lineno">471</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L472"></a><tt class="py-lineno">472</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">less</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">T</tt><tt class="py-op">,</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt><tt class="py-name">theta0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L473"></a><tt class="py-lineno">473</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A time, population size, migration rate, or theta0 '</tt> </tt>
<a name="L474"></a><tt class="py-lineno">474</tt>  <tt class="py-line">                         <tt class="py-string">'is &lt; 0. Has the model been mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L475"></a><tt class="py-lineno">475</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">equal</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">nu</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L476"></a><tt class="py-lineno">476</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A population size is 0. Has the model been '</tt> </tt>
<a name="L477"></a><tt class="py-lineno">477</tt>  <tt class="py-line">                         <tt class="py-string">'mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L478"></a><tt class="py-lineno">478</tt>  <tt class="py-line"> </tt>
<a name="L479"></a><tt class="py-lineno">479</tt>  <tt class="py-line">    <tt class="py-name">M</tt> <tt class="py-op">=</tt> <tt id="link-106" class="py-name" targets="Function dadi.Integration._Mfunc1D()=dadi.Integration-module.html#_Mfunc1D"><a title="dadi.Integration._Mfunc1D" class="py-name" href="#" onclick="return doclink('link-106', '_Mfunc1D', 'link-106');">_Mfunc1D</a></tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt> </tt>
<a name="L480"></a><tt class="py-lineno">480</tt>  <tt class="py-line">    <tt class="py-name">MInt</tt> <tt class="py-op">=</tt> <tt id="link-107" class="py-name"><a title="dadi.Integration._Mfunc1D" class="py-name" href="#" onclick="return doclink('link-107', '_Mfunc1D', 'link-106');">_Mfunc1D</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">)</tt> </tt>
<a name="L481"></a><tt class="py-lineno">481</tt>  <tt class="py-line">    <tt class="py-name">V</tt> <tt class="py-op">=</tt> <tt id="link-108" class="py-name" targets="Function dadi.Integration._Vfunc()=dadi.Integration-module.html#_Vfunc"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-108', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">=</tt><tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
<a name="L482"></a><tt class="py-lineno">482</tt>  <tt class="py-line">    <tt class="py-name">VInt</tt> <tt class="py-op">=</tt> <tt id="link-109" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-109', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">=</tt><tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
<a name="L483"></a><tt class="py-lineno">483</tt>  <tt class="py-line"> </tt>
<a name="L484"></a><tt class="py-lineno">484</tt>  <tt class="py-line">    <tt class="py-name">dx</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">)</tt> </tt>
<a name="L485"></a><tt class="py-lineno">485</tt>  <tt class="py-line">    <tt class="py-name">dfactor</tt> <tt class="py-op">=</tt> <tt id="link-110" class="py-name" targets="Function dadi.Integration._compute_dfactor()=dadi.Integration-module.html#_compute_dfactor"><a title="dadi.Integration._compute_dfactor" class="py-name" href="#" onclick="return doclink('link-110', '_compute_dfactor', 'link-110');">_compute_dfactor</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt> </tt>
<a name="L486"></a><tt class="py-lineno">486</tt>  <tt class="py-line">    <tt class="py-name">delj</tt> <tt class="py-op">=</tt> <tt id="link-111" class="py-name" targets="Function dadi.Integration._compute_delj()=dadi.Integration-module.html#_compute_delj"><a title="dadi.Integration._compute_delj" class="py-name" href="#" onclick="return doclink('link-111', '_compute_delj', 'link-111');">_compute_delj</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt> <tt class="py-name">MInt</tt><tt class="py-op">,</tt> <tt class="py-name">VInt</tt><tt class="py-op">)</tt> </tt>
<a name="L487"></a><tt class="py-lineno">487</tt>  <tt class="py-line"> </tt>
<a name="L488"></a><tt class="py-lineno">488</tt>  <tt class="py-line">    <tt class="py-name">a</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> </tt>
<a name="L489"></a><tt class="py-lineno">489</tt>  <tt class="py-line">    <tt class="py-name">a</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MInt</tt> <tt class="py-op">*</tt> <tt class="py-name">delj</tt> <tt class="py-op">-</tt> <tt class="py-name">V</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L490"></a><tt class="py-lineno">490</tt>  <tt class="py-line"> </tt>
<a name="L491"></a><tt class="py-lineno">491</tt>  <tt class="py-line">    <tt class="py-name">c</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> </tt>
<a name="L492"></a><tt class="py-lineno">492</tt>  <tt class="py-line">    <tt class="py-name">c</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MInt</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">delj</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">V</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L493"></a><tt class="py-lineno">493</tt>  <tt class="py-line"> </tt>
<a name="L494"></a><tt class="py-lineno">494</tt>  <tt class="py-line">    <tt class="py-name">b</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> </tt>
<a name="L495"></a><tt class="py-lineno">495</tt>  <tt class="py-line">    <tt class="py-name">b</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MInt</tt> <tt class="py-op">*</tt> <tt class="py-name">delj</tt> <tt class="py-op">-</tt> <tt class="py-name">V</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L496"></a><tt class="py-lineno">496</tt>  <tt class="py-line">    <tt class="py-name">b</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MInt</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">delj</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">V</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L497"></a><tt class="py-lineno">497</tt>  <tt class="py-line"> </tt>
<a name="L498"></a><tt class="py-lineno">498</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt><tt class="py-op">(</tt><tt class="py-name">M</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">&lt;=</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L499"></a><tt class="py-lineno">499</tt>  <tt class="py-line">        <tt class="py-name">b</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">(</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu</tt> <tt class="py-op">-</tt> <tt class="py-name">M</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L500"></a><tt class="py-lineno">500</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt><tt class="py-op">(</tt><tt class="py-name">M</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">&gt;=</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L501"></a><tt class="py-lineno">501</tt>  <tt class="py-line">        <tt class="py-name">b</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu</tt> <tt class="py-op">-</tt> <tt class="py-name">M</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L502"></a><tt class="py-lineno">502</tt>  <tt class="py-line"> </tt>
<a name="L503"></a><tt class="py-lineno">503</tt>  <tt class="py-line">    <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt id="link-112" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-112', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma</tt><tt class="py-op">,</tt><tt class="py-name">h</tt><tt class="py-op">)</tt> </tt>
<a name="L504"></a><tt class="py-lineno">504</tt>  <tt class="py-line">    <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">initial_t</tt> </tt>
<a name="L505"></a><tt class="py-lineno">505</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">current_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">T</tt><tt class="py-op">:</tt>     </tt>
<a name="L506"></a><tt class="py-lineno">506</tt>  <tt class="py-line">        <tt class="py-name">this_dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt class="py-name">dt</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L507"></a><tt class="py-lineno">507</tt>  <tt class="py-line"> </tt>
<a name="L508"></a><tt class="py-lineno">508</tt>  <tt class="py-line">        <tt id="link-113" class="py-name"><a title="dadi.Integration._inject_mutations_1D" class="py-name" href="#" onclick="return doclink('link-113', '_inject_mutations_1D', 'link-29');">_inject_mutations_1D</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">)</tt> </tt>
<a name="L509"></a><tt class="py-lineno">509</tt>  <tt class="py-line">        <tt class="py-name">r</tt> <tt class="py-op">=</tt> <tt class="py-name">phi</tt><tt class="py-op">/</tt><tt class="py-name">this_dt</tt> </tt>
<a name="L510"></a><tt class="py-lineno">510</tt>  <tt class="py-line">        <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt id="link-114" class="py-name"><a title="dadi.tridiag
dadi.tridiag.tridiag" class="py-name" href="#" onclick="return doclink('link-114', 'tridiag', 'link-4');">tridiag</a></tt><tt class="py-op">.</tt><tt id="link-115" class="py-name"><a title="dadi.tridiag
dadi.tridiag.tridiag" class="py-name" href="#" onclick="return doclink('link-115', 'tridiag', 'link-4');">tridiag</a></tt><tt class="py-op">(</tt><tt class="py-name">a</tt><tt class="py-op">,</tt> <tt class="py-name">b</tt><tt class="py-op">+</tt><tt class="py-number">1</tt><tt class="py-op">/</tt><tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt class="py-name">c</tt><tt class="py-op">,</tt> <tt class="py-name">r</tt><tt class="py-op">)</tt> </tt>
<a name="L511"></a><tt class="py-lineno">511</tt>  <tt class="py-line">        <tt class="py-name">current_t</tt> <tt class="py-op">+=</tt> <tt class="py-name">this_dt</tt> </tt>
<a name="L512"></a><tt class="py-lineno">512</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="L513"></a><tt class="py-lineno">513</tt>  <tt class="py-line"> </tt>
<a name="_two_pops_const_params"></a><div id="_two_pops_const_params-def"><a name="L514"></a><tt class="py-lineno">514</tt> <a class="py-toggle" href="#" id="_two_pops_const_params-toggle" onclick="return toggle('_two_pops_const_params');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_two_pops_const_params">_two_pops_const_params</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">T</tt><tt class="py-op">,</tt> <tt class="py-param">nu1</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-param">nu2</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">m12</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m21</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> </tt>
<a name="L515"></a><tt class="py-lineno">515</tt>  <tt class="py-line">                           <tt class="py-param">gamma1</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">gamma2</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">h1</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">h2</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt>  </tt>
<a name="L516"></a><tt class="py-lineno">516</tt>  <tt class="py-line">                           <tt class="py-param">initial_t</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">frozen1</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> <tt class="py-param">frozen2</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_two_pops_const_params-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_two_pops_const_params-expanded"><a name="L517"></a><tt class="py-lineno">517</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L518"></a><tt class="py-lineno">518</tt>  <tt class="py-line"><tt class="py-docstring">    Integrate two populations with constant parameters.</tt> </tt>
<a name="L519"></a><tt class="py-lineno">519</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L520"></a><tt class="py-lineno">520</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">less</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">T</tt><tt class="py-op">,</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">theta0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L521"></a><tt class="py-lineno">521</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A time, population size, migration rate, or theta0 '</tt> </tt>
<a name="L522"></a><tt class="py-lineno">522</tt>  <tt class="py-line">                         <tt class="py-string">'is &lt; 0. Has the model been mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L523"></a><tt class="py-lineno">523</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">equal</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L524"></a><tt class="py-lineno">524</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A population size is 0. Has the model been '</tt> </tt>
<a name="L525"></a><tt class="py-lineno">525</tt>  <tt class="py-line">                         <tt class="py-string">'mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L526"></a><tt class="py-lineno">526</tt>  <tt class="py-line">    <tt class="py-name">yy</tt> <tt class="py-op">=</tt> <tt class="py-name">xx</tt> </tt>
<a name="L527"></a><tt class="py-lineno">527</tt>  <tt class="py-line"> </tt>
<a name="L528"></a><tt class="py-lineno">528</tt>  <tt class="py-line">    <tt class="py-comment"># The use of nuax (= numpy.newaxis) here is for memory conservation. We</tt> </tt>
<a name="L529"></a><tt class="py-lineno">529</tt>  <tt class="py-line">    <tt class="py-comment"># could just create big X and Y arrays which only varied along one axis,</tt> </tt>
<a name="L530"></a><tt class="py-lineno">530</tt>  <tt class="py-line">    <tt class="py-comment"># but that would be wasteful.</tt> </tt>
<a name="L531"></a><tt class="py-lineno">531</tt>  <tt class="py-line">    <tt class="py-name">Vx</tt> <tt class="py-op">=</tt> <tt id="link-116" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-116', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">nu1</tt><tt class="py-op">)</tt> </tt>
<a name="L532"></a><tt class="py-lineno">532</tt>  <tt class="py-line">    <tt class="py-name">VxInt</tt> <tt class="py-op">=</tt> <tt id="link-117" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-117', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">+</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">nu1</tt><tt class="py-op">)</tt> </tt>
<a name="L533"></a><tt class="py-lineno">533</tt>  <tt class="py-line">    <tt class="py-name">Mx</tt> <tt class="py-op">=</tt> <tt id="link-118" class="py-name" targets="Function dadi.Integration._Mfunc2D()=dadi.Integration-module.html#_Mfunc2D"><a title="dadi.Integration._Mfunc2D" class="py-name" href="#" onclick="return doclink('link-118', '_Mfunc2D', 'link-118');">_Mfunc2D</a></tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">m12</tt><tt class="py-op">,</tt> <tt class="py-name">gamma1</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt><tt class="py-op">)</tt> </tt>
<a name="L534"></a><tt class="py-lineno">534</tt>  <tt class="py-line">    <tt class="py-name">MxInt</tt> <tt class="py-op">=</tt> <tt id="link-119" class="py-name"><a title="dadi.Integration._Mfunc2D" class="py-name" href="#" onclick="return doclink('link-119', '_Mfunc2D', 'link-118');">_Mfunc2D</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">+</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">m12</tt><tt class="py-op">,</tt> <tt class="py-name">gamma1</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt><tt class="py-op">)</tt> </tt>
<a name="L535"></a><tt class="py-lineno">535</tt>  <tt class="py-line"> </tt>
<a name="L536"></a><tt class="py-lineno">536</tt>  <tt class="py-line">    <tt class="py-name">Vy</tt> <tt class="py-op">=</tt> <tt id="link-120" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-120', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">nu2</tt><tt class="py-op">)</tt> </tt>
<a name="L537"></a><tt class="py-lineno">537</tt>  <tt class="py-line">    <tt class="py-name">VyInt</tt> <tt class="py-op">=</tt> <tt id="link-121" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-121', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">+</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">nu2</tt><tt class="py-op">)</tt> </tt>
<a name="L538"></a><tt class="py-lineno">538</tt>  <tt class="py-line">    <tt class="py-name">My</tt> <tt class="py-op">=</tt> <tt id="link-122" class="py-name"><a title="dadi.Integration._Mfunc2D" class="py-name" href="#" onclick="return doclink('link-122', '_Mfunc2D', 'link-118');">_Mfunc2D</a></tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">m21</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2</tt><tt class="py-op">,</tt> <tt class="py-name">h2</tt><tt class="py-op">)</tt> </tt>
<a name="L539"></a><tt class="py-lineno">539</tt>  <tt class="py-line">    <tt class="py-name">MyInt</tt> <tt class="py-op">=</tt> <tt id="link-123" class="py-name"><a title="dadi.Integration._Mfunc2D" class="py-name" href="#" onclick="return doclink('link-123', '_Mfunc2D', 'link-118');">_Mfunc2D</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">m21</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">)</tt> </tt>
<a name="L540"></a><tt class="py-lineno">540</tt>  <tt class="py-line"> </tt>
<a name="L541"></a><tt class="py-lineno">541</tt>  <tt class="py-line">    <tt class="py-name">dx</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">)</tt> </tt>
<a name="L542"></a><tt class="py-lineno">542</tt>  <tt class="py-line">    <tt class="py-name">dfact_x</tt> <tt class="py-op">=</tt> <tt id="link-124" class="py-name"><a title="dadi.Integration._compute_dfactor" class="py-name" href="#" onclick="return doclink('link-124', '_compute_dfactor', 'link-110');">_compute_dfactor</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt> </tt>
<a name="L543"></a><tt class="py-lineno">543</tt>  <tt class="py-line">    <tt class="py-name">deljx</tt> <tt class="py-op">=</tt> <tt id="link-125" class="py-name"><a title="dadi.Integration._compute_delj" class="py-name" href="#" onclick="return doclink('link-125', '_compute_delj', 'link-111');">_compute_delj</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt> <tt class="py-name">MxInt</tt><tt class="py-op">,</tt> <tt class="py-name">VxInt</tt><tt class="py-op">)</tt> </tt>
<a name="L544"></a><tt class="py-lineno">544</tt>  <tt class="py-line"> </tt>
<a name="L545"></a><tt class="py-lineno">545</tt>  <tt class="py-line">    <tt class="py-name">dy</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">)</tt> </tt>
<a name="L546"></a><tt class="py-lineno">546</tt>  <tt class="py-line">    <tt class="py-name">dfact_y</tt> <tt class="py-op">=</tt> <tt id="link-126" class="py-name"><a title="dadi.Integration._compute_dfactor" class="py-name" href="#" onclick="return doclink('link-126', '_compute_dfactor', 'link-110');">_compute_dfactor</a></tt><tt class="py-op">(</tt><tt class="py-name">dy</tt><tt class="py-op">)</tt> </tt>
<a name="L547"></a><tt class="py-lineno">547</tt>  <tt class="py-line">    <tt class="py-name">deljy</tt> <tt class="py-op">=</tt> <tt id="link-127" class="py-name"><a title="dadi.Integration._compute_delj" class="py-name" href="#" onclick="return doclink('link-127', '_compute_delj', 'link-111');">_compute_delj</a></tt><tt class="py-op">(</tt><tt class="py-name">dy</tt><tt class="py-op">,</tt> <tt class="py-name">MyInt</tt><tt class="py-op">,</tt> <tt class="py-name">VyInt</tt><tt class="py-op">,</tt> <tt class="py-name">axis</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">)</tt> </tt>
<a name="L548"></a><tt class="py-lineno">548</tt>  <tt class="py-line"> </tt>
<a name="L549"></a><tt class="py-lineno">549</tt>  <tt class="py-line">    <tt class="py-comment"># The nuax's here broadcast the our various arrays to have the proper shape</tt> </tt>
<a name="L550"></a><tt class="py-lineno">550</tt>  <tt class="py-line">    <tt class="py-comment"># to fit into ax,bx,cx</tt> </tt>
<a name="L551"></a><tt class="py-lineno">551</tt>  <tt class="py-line">    <tt class="py-name">ax</tt><tt class="py-op">,</tt> <tt class="py-name">bx</tt><tt class="py-op">,</tt> <tt class="py-name">cx</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">ii</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L552"></a><tt class="py-lineno">552</tt>  <tt class="py-line">    <tt class="py-name">ax</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_x</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MxInt</tt><tt class="py-op">*</tt><tt class="py-name">deljx</tt>    <tt class="py-op">-</tt> <tt class="py-name">Vx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L553"></a><tt class="py-lineno">553</tt>  <tt class="py-line">    <tt class="py-name">cx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_x</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MxInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljx</tt><tt class="py-op">)</tt><tt class="py-op">-</tt> <tt class="py-name">Vx</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L554"></a><tt class="py-lineno">554</tt>  <tt class="py-line">    <tt class="py-name">bx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_x</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MxInt</tt><tt class="py-op">*</tt><tt class="py-name">deljx</tt>    <tt class="py-op">+</tt> <tt class="py-name">Vx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L555"></a><tt class="py-lineno">555</tt>  <tt class="py-line">    <tt class="py-name">bx</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_x</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MxInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljx</tt><tt class="py-op">)</tt><tt class="py-op">+</tt> <tt class="py-name">Vx</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L556"></a><tt class="py-lineno">556</tt>  <tt class="py-line"> </tt>
<a name="L557"></a><tt class="py-lineno">557</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">Mx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">&lt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L558"></a><tt class="py-lineno">558</tt>  <tt class="py-line">        <tt class="py-name">bx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">(</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu1</tt> <tt class="py-op">-</tt> <tt class="py-name">Mx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L559"></a><tt class="py-lineno">559</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">Mx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">&gt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L560"></a><tt class="py-lineno">560</tt>  <tt class="py-line">        <tt class="py-name">bx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu1</tt> <tt class="py-op">-</tt> <tt class="py-name">Mx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L561"></a><tt class="py-lineno">561</tt>  <tt class="py-line"> </tt>
<a name="L562"></a><tt class="py-lineno">562</tt>  <tt class="py-line">    <tt class="py-name">ay</tt><tt class="py-op">,</tt> <tt class="py-name">by</tt><tt class="py-op">,</tt> <tt class="py-name">cy</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">ii</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L563"></a><tt class="py-lineno">563</tt>  <tt class="py-line">    <tt class="py-name">ay</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_y</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MyInt</tt><tt class="py-op">*</tt><tt class="py-name">deljy</tt>     <tt class="py-op">-</tt> <tt class="py-name">Vy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dy</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L564"></a><tt class="py-lineno">564</tt>  <tt class="py-line">    <tt class="py-name">cy</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_y</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MyInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljy</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">Vy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dy</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L565"></a><tt class="py-lineno">565</tt>  <tt class="py-line">    <tt class="py-name">by</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_y</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MyInt</tt><tt class="py-op">*</tt><tt class="py-name">deljy</tt>     <tt class="py-op">+</tt> <tt class="py-name">Vy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dy</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L566"></a><tt class="py-lineno">566</tt>  <tt class="py-line">    <tt class="py-name">by</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_y</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MyInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljy</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">Vy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dy</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L567"></a><tt class="py-lineno">567</tt>  <tt class="py-line"> </tt>
<a name="L568"></a><tt class="py-lineno">568</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">My</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">&lt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L569"></a><tt class="py-lineno">569</tt>  <tt class="py-line">        <tt class="py-name">by</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">(</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu2</tt> <tt class="py-op">-</tt> <tt class="py-name">My</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dy</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L570"></a><tt class="py-lineno">570</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">My</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">&gt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L571"></a><tt class="py-lineno">571</tt>  <tt class="py-line">        <tt class="py-name">by</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu2</tt> <tt class="py-op">-</tt> <tt class="py-name">My</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dy</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L572"></a><tt class="py-lineno">572</tt>  <tt class="py-line"> </tt>
<a name="L573"></a><tt class="py-lineno">573</tt>  <tt class="py-line">    <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt id="link-128" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-128', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m12</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">h1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> </tt>
<a name="L574"></a><tt class="py-lineno">574</tt>  <tt class="py-line">             <tt id="link-129" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-129', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dy</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m21</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L575"></a><tt class="py-lineno">575</tt>  <tt class="py-line">    <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">initial_t</tt> </tt>
<a name="L576"></a><tt class="py-lineno">576</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">current_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">T</tt><tt class="py-op">:</tt>     </tt>
<a name="L577"></a><tt class="py-lineno">577</tt>  <tt class="py-line">        <tt class="py-name">this_dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt class="py-name">dt</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L578"></a><tt class="py-lineno">578</tt>  <tt class="py-line">        <tt id="link-130" class="py-name"><a title="dadi.Integration._inject_mutations_2D" class="py-name" href="#" onclick="return doclink('link-130', '_inject_mutations_2D', 'link-54');">_inject_mutations_2D</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">,</tt> <tt class="py-name">frozen1</tt><tt class="py-op">,</tt> <tt class="py-name">frozen2</tt><tt class="py-op">)</tt> </tt>
<a name="L579"></a><tt class="py-lineno">579</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen1</tt><tt class="py-op">:</tt> </tt>
<a name="L580"></a><tt class="py-lineno">580</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-131" class="py-name" targets="Variable dadi.integration_c.implicit_precalc_2Dx=dadi.integration_c-module.html#implicit_precalc_2Dx"><a title="dadi.integration_c.implicit_precalc_2Dx" class="py-name" href="#" onclick="return doclink('link-131', 'implicit_precalc_2Dx', 'link-131');">implicit_precalc_2Dx</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">ax</tt><tt class="py-op">,</tt> <tt class="py-name">bx</tt><tt class="py-op">,</tt> <tt class="py-name">cx</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">)</tt> </tt>
<a name="L581"></a><tt class="py-lineno">581</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen2</tt><tt class="py-op">:</tt> </tt>
<a name="L582"></a><tt class="py-lineno">582</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-132" class="py-name" targets="Variable dadi.integration_c.implicit_precalc_2Dy=dadi.integration_c-module.html#implicit_precalc_2Dy"><a title="dadi.integration_c.implicit_precalc_2Dy" class="py-name" href="#" onclick="return doclink('link-132', 'implicit_precalc_2Dy', 'link-132');">implicit_precalc_2Dy</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">ay</tt><tt class="py-op">,</tt> <tt class="py-name">by</tt><tt class="py-op">,</tt> <tt class="py-name">cy</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">)</tt> </tt>
<a name="L583"></a><tt class="py-lineno">583</tt>  <tt class="py-line">        <tt class="py-name">current_t</tt> <tt class="py-op">+=</tt> <tt class="py-name">this_dt</tt> </tt>
<a name="L584"></a><tt class="py-lineno">584</tt>  <tt class="py-line"> </tt>
<a name="L585"></a><tt class="py-lineno">585</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="L586"></a><tt class="py-lineno">586</tt>  <tt class="py-line"> </tt>
<a name="_three_pops_const_params"></a><div id="_three_pops_const_params-def"><a name="L587"></a><tt class="py-lineno">587</tt> <a class="py-toggle" href="#" id="_three_pops_const_params-toggle" onclick="return toggle('_three_pops_const_params');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_three_pops_const_params">_three_pops_const_params</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">T</tt><tt class="py-op">,</tt> <tt class="py-param">nu1</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">nu2</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">nu3</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt>  </tt>
<a name="L588"></a><tt class="py-lineno">588</tt>  <tt class="py-line">                             <tt class="py-param">m12</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m13</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m21</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m23</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m31</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">m32</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt>  </tt>
<a name="L589"></a><tt class="py-lineno">589</tt>  <tt class="py-line">                             <tt class="py-param">gamma1</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">gamma2</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">gamma3</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt>  </tt>
<a name="L590"></a><tt class="py-lineno">590</tt>  <tt class="py-line">                             <tt class="py-param">h1</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">h2</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">h3</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">initial_t</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> </tt>
<a name="L591"></a><tt class="py-lineno">591</tt>  <tt class="py-line">                             <tt class="py-param">frozen1</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> <tt class="py-param">frozen2</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">,</tt> <tt class="py-param">frozen3</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_three_pops_const_params-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_three_pops_const_params-expanded"><a name="L592"></a><tt class="py-lineno">592</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L593"></a><tt class="py-lineno">593</tt>  <tt class="py-line"><tt class="py-docstring">    Integrate three population with constant parameters.</tt> </tt>
<a name="L594"></a><tt class="py-lineno">594</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L595"></a><tt class="py-lineno">595</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">less</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">T</tt><tt class="py-op">,</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt><tt class="py-op">,</tt><tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m13</tt><tt class="py-op">,</tt><tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">m23</tt><tt class="py-op">,</tt><tt class="py-name">m31</tt><tt class="py-op">,</tt><tt class="py-name">m32</tt><tt class="py-op">,</tt><tt class="py-name">theta0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L596"></a><tt class="py-lineno">596</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A time, population size, migration rate, or theta0 '</tt> </tt>
<a name="L597"></a><tt class="py-lineno">597</tt>  <tt class="py-line">                         <tt class="py-string">'is &lt; 0. Has the model been mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L598"></a><tt class="py-lineno">598</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">equal</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L599"></a><tt class="py-lineno">599</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A population size is 0. Has the model been '</tt> </tt>
<a name="L600"></a><tt class="py-lineno">600</tt>  <tt class="py-line">                         <tt class="py-string">'mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L601"></a><tt class="py-lineno">601</tt>  <tt class="py-line">    <tt class="py-name">zz</tt> <tt class="py-op">=</tt> <tt class="py-name">yy</tt> <tt class="py-op">=</tt> <tt class="py-name">xx</tt> </tt>
<a name="L602"></a><tt class="py-lineno">602</tt>  <tt class="py-line"> </tt>
<a name="L603"></a><tt class="py-lineno">603</tt>  <tt class="py-line">    <tt class="py-name">Vx</tt> <tt class="py-op">=</tt> <tt id="link-133" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-133', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">nu1</tt><tt class="py-op">)</tt> </tt>
<a name="L604"></a><tt class="py-lineno">604</tt>  <tt class="py-line">    <tt class="py-name">VxInt</tt> <tt class="py-op">=</tt> <tt id="link-134" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-134', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">+</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">nu1</tt><tt class="py-op">)</tt> </tt>
<a name="L605"></a><tt class="py-lineno">605</tt>  <tt class="py-line">    <tt class="py-name">Mx</tt> <tt class="py-op">=</tt> <tt id="link-135" class="py-name" targets="Function dadi.Integration._Mfunc3D()=dadi.Integration-module.html#_Mfunc3D"><a title="dadi.Integration._Mfunc3D" class="py-name" href="#" onclick="return doclink('link-135', '_Mfunc3D', 'link-135');">_Mfunc3D</a></tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt>  </tt>
<a name="L606"></a><tt class="py-lineno">606</tt>  <tt class="py-line">                 <tt class="py-name">m12</tt><tt class="py-op">,</tt> <tt class="py-name">m13</tt><tt class="py-op">,</tt> <tt class="py-name">gamma1</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt><tt class="py-op">)</tt> </tt>
<a name="L607"></a><tt class="py-lineno">607</tt>  <tt class="py-line">    <tt class="py-name">MxInt</tt> <tt class="py-op">=</tt> <tt id="link-136" class="py-name"><a title="dadi.Integration._Mfunc3D" class="py-name" href="#" onclick="return doclink('link-136', '_Mfunc3D', 'link-135');">_Mfunc3D</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">+</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt>  </tt>
<a name="L608"></a><tt class="py-lineno">608</tt>  <tt class="py-line">                    <tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">m12</tt><tt class="py-op">,</tt> <tt class="py-name">m13</tt><tt class="py-op">,</tt> <tt class="py-name">gamma1</tt><tt class="py-op">,</tt> <tt class="py-name">h1</tt><tt class="py-op">)</tt> </tt>
<a name="L609"></a><tt class="py-lineno">609</tt>  <tt class="py-line"> </tt>
<a name="L610"></a><tt class="py-lineno">610</tt>  <tt class="py-line">    <tt class="py-name">dx</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">)</tt> </tt>
<a name="L611"></a><tt class="py-lineno">611</tt>  <tt class="py-line">    <tt class="py-name">dfact_x</tt> <tt class="py-op">=</tt> <tt id="link-137" class="py-name"><a title="dadi.Integration._compute_dfactor" class="py-name" href="#" onclick="return doclink('link-137', '_compute_dfactor', 'link-110');">_compute_dfactor</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt> </tt>
<a name="L612"></a><tt class="py-lineno">612</tt>  <tt class="py-line">    <tt class="py-name">deljx</tt> <tt class="py-op">=</tt> <tt id="link-138" class="py-name"><a title="dadi.Integration._compute_delj" class="py-name" href="#" onclick="return doclink('link-138', '_compute_delj', 'link-111');">_compute_delj</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt> <tt class="py-name">MxInt</tt><tt class="py-op">,</tt> <tt class="py-name">VxInt</tt><tt class="py-op">)</tt> </tt>
<a name="L613"></a><tt class="py-lineno">613</tt>  <tt class="py-line"> </tt>
<a name="L614"></a><tt class="py-lineno">614</tt>  <tt class="py-line">    <tt class="py-name">ax</tt><tt class="py-op">,</tt> <tt class="py-name">bx</tt><tt class="py-op">,</tt> <tt class="py-name">cx</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">ii</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L615"></a><tt class="py-lineno">615</tt>  <tt class="py-line">    <tt class="py-name">ax</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_x</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MxInt</tt><tt class="py-op">*</tt><tt class="py-name">deljx</tt>     </tt>
<a name="L616"></a><tt class="py-lineno">616</tt>  <tt class="py-line">                                       <tt class="py-op">-</tt> <tt class="py-name">Vx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L617"></a><tt class="py-lineno">617</tt>  <tt class="py-line">    <tt class="py-name">cx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_x</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MxInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljx</tt><tt class="py-op">)</tt> </tt>
<a name="L618"></a><tt class="py-lineno">618</tt>  <tt class="py-line">                                       <tt class="py-op">-</tt> <tt class="py-name">Vx</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L619"></a><tt class="py-lineno">619</tt>  <tt class="py-line">    <tt class="py-name">bx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_x</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MxInt</tt><tt class="py-op">*</tt><tt class="py-name">deljx</tt>     </tt>
<a name="L620"></a><tt class="py-lineno">620</tt>  <tt class="py-line">                                       <tt class="py-op">+</tt> <tt class="py-name">Vx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L621"></a><tt class="py-lineno">621</tt>  <tt class="py-line">    <tt class="py-name">bx</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_x</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MxInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljx</tt><tt class="py-op">)</tt> </tt>
<a name="L622"></a><tt class="py-lineno">622</tt>  <tt class="py-line">                                       <tt class="py-op">+</tt> <tt class="py-name">Vx</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L623"></a><tt class="py-lineno">623</tt>  <tt class="py-line"> </tt>
<a name="L624"></a><tt class="py-lineno">624</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">Mx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">&lt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L625"></a><tt class="py-lineno">625</tt>  <tt class="py-line">        <tt class="py-name">bx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">(</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu1</tt> <tt class="py-op">-</tt> <tt class="py-name">Mx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L626"></a><tt class="py-lineno">626</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">Mx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">&gt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L627"></a><tt class="py-lineno">627</tt>  <tt class="py-line">        <tt class="py-name">bx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu1</tt> <tt class="py-op">-</tt> <tt class="py-name">Mx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L628"></a><tt class="py-lineno">628</tt>  <tt class="py-line"> </tt>
<a name="L629"></a><tt class="py-lineno">629</tt>  <tt class="py-line">    <tt class="py-comment"># Memory consumption can be an issue in 3D, so we delete arrays after we're</tt> </tt>
<a name="L630"></a><tt class="py-lineno">630</tt>  <tt class="py-line">    <tt class="py-comment"># done with them.</tt> </tt>
<a name="L631"></a><tt class="py-lineno">631</tt>  <tt class="py-line">    <tt class="py-keyword">del</tt> <tt class="py-name">Vx</tt><tt class="py-op">,</tt><tt class="py-name">VxInt</tt><tt class="py-op">,</tt><tt class="py-name">Mx</tt><tt class="py-op">,</tt><tt class="py-name">MxInt</tt><tt class="py-op">,</tt><tt class="py-name">deljx</tt> </tt>
<a name="L632"></a><tt class="py-lineno">632</tt>  <tt class="py-line"> </tt>
<a name="L633"></a><tt class="py-lineno">633</tt>  <tt class="py-line">    <tt class="py-name">Vy</tt> <tt class="py-op">=</tt> <tt id="link-139" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-139', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">nu2</tt><tt class="py-op">)</tt> </tt>
<a name="L634"></a><tt class="py-lineno">634</tt>  <tt class="py-line">    <tt class="py-name">VyInt</tt> <tt class="py-op">=</tt> <tt id="link-140" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-140', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">+</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">nu2</tt><tt class="py-op">)</tt> </tt>
<a name="L635"></a><tt class="py-lineno">635</tt>  <tt class="py-line">    <tt class="py-name">My</tt> <tt class="py-op">=</tt> <tt id="link-141" class="py-name"><a title="dadi.Integration._Mfunc3D" class="py-name" href="#" onclick="return doclink('link-141', '_Mfunc3D', 'link-135');">_Mfunc3D</a></tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> </tt>
<a name="L636"></a><tt class="py-lineno">636</tt>  <tt class="py-line">                 <tt class="py-name">m21</tt><tt class="py-op">,</tt> <tt class="py-name">m23</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2</tt><tt class="py-op">,</tt> <tt class="py-name">h2</tt><tt class="py-op">)</tt> </tt>
<a name="L637"></a><tt class="py-lineno">637</tt>  <tt class="py-line">    <tt class="py-name">MyInt</tt> <tt class="py-op">=</tt> <tt id="link-142" class="py-name"><a title="dadi.Integration._Mfunc3D" class="py-name" href="#" onclick="return doclink('link-142', '_Mfunc3D', 'link-135');">_Mfunc3D</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> </tt>
<a name="L638"></a><tt class="py-lineno">638</tt>  <tt class="py-line">                    <tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">m21</tt><tt class="py-op">,</tt> <tt class="py-name">m23</tt><tt class="py-op">,</tt> <tt class="py-name">gamma2</tt><tt class="py-op">,</tt> <tt class="py-name">h2</tt><tt class="py-op">)</tt> </tt>
<a name="L639"></a><tt class="py-lineno">639</tt>  <tt class="py-line"> </tt>
<a name="L640"></a><tt class="py-lineno">640</tt>  <tt class="py-line">    <tt class="py-name">dy</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">yy</tt><tt class="py-op">)</tt> </tt>
<a name="L641"></a><tt class="py-lineno">641</tt>  <tt class="py-line">    <tt class="py-name">dfact_y</tt> <tt class="py-op">=</tt> <tt id="link-143" class="py-name"><a title="dadi.Integration._compute_dfactor" class="py-name" href="#" onclick="return doclink('link-143', '_compute_dfactor', 'link-110');">_compute_dfactor</a></tt><tt class="py-op">(</tt><tt class="py-name">dy</tt><tt class="py-op">)</tt> </tt>
<a name="L642"></a><tt class="py-lineno">642</tt>  <tt class="py-line">    <tt class="py-name">deljy</tt> <tt class="py-op">=</tt> <tt id="link-144" class="py-name"><a title="dadi.Integration._compute_delj" class="py-name" href="#" onclick="return doclink('link-144', '_compute_delj', 'link-111');">_compute_delj</a></tt><tt class="py-op">(</tt><tt class="py-name">dy</tt><tt class="py-op">,</tt> <tt class="py-name">MyInt</tt><tt class="py-op">,</tt> <tt class="py-name">VyInt</tt><tt class="py-op">,</tt> <tt class="py-name">axis</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">)</tt> </tt>
<a name="L643"></a><tt class="py-lineno">643</tt>  <tt class="py-line"> </tt>
<a name="L644"></a><tt class="py-lineno">644</tt>  <tt class="py-line">    <tt class="py-name">ay</tt><tt class="py-op">,</tt> <tt class="py-name">by</tt><tt class="py-op">,</tt> <tt class="py-name">cy</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">ii</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L645"></a><tt class="py-lineno">645</tt>  <tt class="py-line">    <tt class="py-name">ay</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_y</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MyInt</tt><tt class="py-op">*</tt><tt class="py-name">deljy</tt>      </tt>
<a name="L646"></a><tt class="py-lineno">646</tt>  <tt class="py-line">                                    <tt class="py-op">-</tt> <tt class="py-name">Vy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L647"></a><tt class="py-lineno">647</tt>  <tt class="py-line">    <tt class="py-name">cy</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_y</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MyInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljy</tt><tt class="py-op">)</tt>  </tt>
<a name="L648"></a><tt class="py-lineno">648</tt>  <tt class="py-line">                                    <tt class="py-op">-</tt> <tt class="py-name">Vy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L649"></a><tt class="py-lineno">649</tt>  <tt class="py-line">    <tt class="py-name">by</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_y</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MyInt</tt><tt class="py-op">*</tt><tt class="py-name">deljy</tt>      </tt>
<a name="L650"></a><tt class="py-lineno">650</tt>  <tt class="py-line">                                    <tt class="py-op">+</tt> <tt class="py-name">Vy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L651"></a><tt class="py-lineno">651</tt>  <tt class="py-line">    <tt class="py-name">by</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_y</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MyInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljy</tt><tt class="py-op">)</tt>  </tt>
<a name="L652"></a><tt class="py-lineno">652</tt>  <tt class="py-line">                                    <tt class="py-op">+</tt> <tt class="py-name">Vy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L653"></a><tt class="py-lineno">653</tt>  <tt class="py-line"> </tt>
<a name="L654"></a><tt class="py-lineno">654</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">My</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">&lt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L655"></a><tt class="py-lineno">655</tt>  <tt class="py-line">        <tt class="py-name">by</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">(</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu2</tt> <tt class="py-op">-</tt> <tt class="py-name">My</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dy</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L656"></a><tt class="py-lineno">656</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">My</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">&gt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L657"></a><tt class="py-lineno">657</tt>  <tt class="py-line">        <tt class="py-name">by</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu2</tt> <tt class="py-op">-</tt> <tt class="py-name">My</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dy</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L658"></a><tt class="py-lineno">658</tt>  <tt class="py-line"> </tt>
<a name="L659"></a><tt class="py-lineno">659</tt>  <tt class="py-line">    <tt class="py-keyword">del</tt> <tt class="py-name">Vy</tt><tt class="py-op">,</tt><tt class="py-name">VyInt</tt><tt class="py-op">,</tt><tt class="py-name">My</tt><tt class="py-op">,</tt><tt class="py-name">MyInt</tt><tt class="py-op">,</tt><tt class="py-name">deljy</tt> </tt>
<a name="L660"></a><tt class="py-lineno">660</tt>  <tt class="py-line"> </tt>
<a name="L661"></a><tt class="py-lineno">661</tt>  <tt class="py-line">    <tt class="py-name">Vz</tt> <tt class="py-op">=</tt> <tt id="link-145" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-145', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-name">zz</tt><tt class="py-op">,</tt> <tt class="py-name">nu3</tt><tt class="py-op">)</tt> </tt>
<a name="L662"></a><tt class="py-lineno">662</tt>  <tt class="py-line">    <tt class="py-name">VzInt</tt> <tt class="py-op">=</tt> <tt id="link-146" class="py-name"><a title="dadi.Integration._Vfunc" class="py-name" href="#" onclick="return doclink('link-146', '_Vfunc', 'link-108');">_Vfunc</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">+</tt><tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">nu3</tt><tt class="py-op">)</tt> </tt>
<a name="L663"></a><tt class="py-lineno">663</tt>  <tt class="py-line">    <tt class="py-name">Mz</tt> <tt class="py-op">=</tt> <tt id="link-147" class="py-name"><a title="dadi.Integration._Mfunc3D" class="py-name" href="#" onclick="return doclink('link-147', '_Mfunc3D', 'link-135');">_Mfunc3D</a></tt><tt class="py-op">(</tt><tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> </tt>
<a name="L664"></a><tt class="py-lineno">664</tt>  <tt class="py-line">                 <tt class="py-name">m31</tt><tt class="py-op">,</tt> <tt class="py-name">m32</tt><tt class="py-op">,</tt> <tt class="py-name">gamma3</tt><tt class="py-op">,</tt> <tt class="py-name">h3</tt><tt class="py-op">)</tt> </tt>
<a name="L665"></a><tt class="py-lineno">665</tt>  <tt class="py-line">    <tt class="py-name">MzInt</tt> <tt class="py-op">=</tt> <tt id="link-148" class="py-name"><a title="dadi.Integration._Mfunc3D" class="py-name" href="#" onclick="return doclink('link-148', '_Mfunc3D', 'link-135');">_Mfunc3D</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">zz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> </tt>
<a name="L666"></a><tt class="py-lineno">666</tt>  <tt class="py-line">                    <tt class="py-name">yy</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-name">m31</tt><tt class="py-op">,</tt> <tt class="py-name">m32</tt><tt class="py-op">,</tt> <tt class="py-name">gamma3</tt><tt class="py-op">,</tt> <tt class="py-name">h3</tt><tt class="py-op">)</tt> </tt>
<a name="L667"></a><tt class="py-lineno">667</tt>  <tt class="py-line"> </tt>
<a name="L668"></a><tt class="py-lineno">668</tt>  <tt class="py-line">    <tt class="py-name">dz</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">zz</tt><tt class="py-op">)</tt> </tt>
<a name="L669"></a><tt class="py-lineno">669</tt>  <tt class="py-line">    <tt class="py-name">dfact_z</tt> <tt class="py-op">=</tt> <tt id="link-149" class="py-name"><a title="dadi.Integration._compute_dfactor" class="py-name" href="#" onclick="return doclink('link-149', '_compute_dfactor', 'link-110');">_compute_dfactor</a></tt><tt class="py-op">(</tt><tt class="py-name">dz</tt><tt class="py-op">)</tt> </tt>
<a name="L670"></a><tt class="py-lineno">670</tt>  <tt class="py-line">    <tt class="py-name">deljz</tt> <tt class="py-op">=</tt> <tt id="link-150" class="py-name"><a title="dadi.Integration._compute_delj" class="py-name" href="#" onclick="return doclink('link-150', '_compute_delj', 'link-111');">_compute_delj</a></tt><tt class="py-op">(</tt><tt class="py-name">dz</tt><tt class="py-op">,</tt> <tt class="py-name">MzInt</tt><tt class="py-op">,</tt> <tt class="py-name">VzInt</tt><tt class="py-op">,</tt> <tt class="py-name">axis</tt><tt class="py-op">=</tt><tt class="py-number">2</tt><tt class="py-op">)</tt> </tt>
<a name="L671"></a><tt class="py-lineno">671</tt>  <tt class="py-line"> </tt>
<a name="L672"></a><tt class="py-lineno">672</tt>  <tt class="py-line">    <tt class="py-name">az</tt><tt class="py-op">,</tt> <tt class="py-name">bz</tt><tt class="py-op">,</tt> <tt class="py-name">cz</tt> <tt class="py-op">=</tt> <tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">ii</tt> <tt class="py-keyword">in</tt> <tt class="py-name">range</tt><tt class="py-op">(</tt><tt class="py-number">3</tt><tt class="py-op">)</tt><tt class="py-op">]</tt> </tt>
<a name="L673"></a><tt class="py-lineno">673</tt>  <tt class="py-line">    <tt class="py-name">az</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_z</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MzInt</tt><tt class="py-op">*</tt><tt class="py-name">deljz</tt>     <tt class="py-op">-</tt> <tt class="py-name">Vz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dz</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L674"></a><tt class="py-lineno">674</tt>  <tt class="py-line">    <tt class="py-name">cz</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_z</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MzInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljz</tt><tt class="py-op">)</tt> <tt class="py-op">-</tt> <tt class="py-name">Vz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dz</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L675"></a><tt class="py-lineno">675</tt>  <tt class="py-line">    <tt class="py-name">bz</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_z</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt> <tt class="py-name">MzInt</tt><tt class="py-op">*</tt><tt class="py-name">deljz</tt>     <tt class="py-op">+</tt> <tt class="py-name">Vz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dz</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L676"></a><tt class="py-lineno">676</tt>  <tt class="py-line">    <tt class="py-name">bz</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">,</tt><tt class="py-op">:</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfact_z</tt><tt class="py-op">[</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MzInt</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">deljz</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">Vz</tt><tt class="py-op">[</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt><tt class="py-name">nuax</tt><tt class="py-op">,</tt> <tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dz</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L677"></a><tt class="py-lineno">677</tt>  <tt class="py-line"> </tt>
<a name="L678"></a><tt class="py-lineno">678</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">Mz</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">&lt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L679"></a><tt class="py-lineno">679</tt>  <tt class="py-line">        <tt class="py-name">bz</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">(</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu3</tt> <tt class="py-op">-</tt> <tt class="py-name">Mz</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">,</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dz</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L680"></a><tt class="py-lineno">680</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">Mz</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">&gt;=</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L681"></a><tt class="py-lineno">681</tt>  <tt class="py-line">        <tt class="py-name">bz</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu3</tt> <tt class="py-op">-</tt> <tt class="py-name">Mz</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">,</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dz</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L682"></a><tt class="py-lineno">682</tt>  <tt class="py-line"> </tt>
<a name="L683"></a><tt class="py-lineno">683</tt>  <tt class="py-line">    <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt id="link-151" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-151', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">nu1</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m12</tt><tt class="py-op">,</tt><tt class="py-name">m13</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma1</tt><tt class="py-op">,</tt><tt class="py-name">h1</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> </tt>
<a name="L684"></a><tt class="py-lineno">684</tt>  <tt class="py-line">             <tt id="link-152" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-152', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dy</tt><tt class="py-op">,</tt><tt class="py-name">nu2</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m21</tt><tt class="py-op">,</tt><tt class="py-name">m23</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma2</tt><tt class="py-op">,</tt><tt class="py-name">h2</tt><tt class="py-op">)</tt><tt class="py-op">,</tt> </tt>
<a name="L685"></a><tt class="py-lineno">685</tt>  <tt class="py-line">             <tt id="link-153" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-153', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dz</tt><tt class="py-op">,</tt><tt class="py-name">nu3</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-name">m31</tt><tt class="py-op">,</tt><tt class="py-name">m32</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma3</tt><tt class="py-op">,</tt><tt class="py-name">h3</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L686"></a><tt class="py-lineno">686</tt>  <tt class="py-line">    <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">initial_t</tt> </tt>
<a name="L687"></a><tt class="py-lineno">687</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">current_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">T</tt><tt class="py-op">:</tt>     </tt>
<a name="L688"></a><tt class="py-lineno">688</tt>  <tt class="py-line">        <tt class="py-name">this_dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt class="py-name">dt</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L689"></a><tt class="py-lineno">689</tt>  <tt class="py-line">        <tt id="link-154" class="py-name"><a title="dadi.Integration._inject_mutations_3D" class="py-name" href="#" onclick="return doclink('link-154', '_inject_mutations_3D', 'link-98');">_inject_mutations_3D</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">yy</tt><tt class="py-op">,</tt> <tt class="py-name">zz</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">,</tt> </tt>
<a name="L690"></a><tt class="py-lineno">690</tt>  <tt class="py-line">                             <tt class="py-name">frozen1</tt><tt class="py-op">,</tt> <tt class="py-name">frozen2</tt><tt class="py-op">,</tt> <tt class="py-name">frozen3</tt><tt class="py-op">)</tt> </tt>
<a name="L691"></a><tt class="py-lineno">691</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen1</tt><tt class="py-op">:</tt> </tt>
<a name="L692"></a><tt class="py-lineno">692</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-155" class="py-name" targets="Variable dadi.integration_c.implicit_precalc_3Dx=dadi.integration_c-module.html#implicit_precalc_3Dx"><a title="dadi.integration_c.implicit_precalc_3Dx" class="py-name" href="#" onclick="return doclink('link-155', 'implicit_precalc_3Dx', 'link-155');">implicit_precalc_3Dx</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">ax</tt><tt class="py-op">,</tt> <tt class="py-name">bx</tt><tt class="py-op">,</tt> <tt class="py-name">cx</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">)</tt> </tt>
<a name="L693"></a><tt class="py-lineno">693</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen2</tt><tt class="py-op">:</tt> </tt>
<a name="L694"></a><tt class="py-lineno">694</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-156" class="py-name" targets="Variable dadi.integration_c.implicit_precalc_3Dy=dadi.integration_c-module.html#implicit_precalc_3Dy"><a title="dadi.integration_c.implicit_precalc_3Dy" class="py-name" href="#" onclick="return doclink('link-156', 'implicit_precalc_3Dy', 'link-156');">implicit_precalc_3Dy</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">ay</tt><tt class="py-op">,</tt> <tt class="py-name">by</tt><tt class="py-op">,</tt> <tt class="py-name">cy</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">)</tt> </tt>
<a name="L695"></a><tt class="py-lineno">695</tt>  <tt class="py-line">        <tt class="py-keyword">if</tt> <tt class="py-keyword">not</tt> <tt class="py-name">frozen3</tt><tt class="py-op">:</tt> </tt>
<a name="L696"></a><tt class="py-lineno">696</tt>  <tt class="py-line">            <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">int_c</tt><tt class="py-op">.</tt><tt id="link-157" class="py-name" targets="Variable dadi.integration_c.implicit_precalc_3Dz=dadi.integration_c-module.html#implicit_precalc_3Dz"><a title="dadi.integration_c.implicit_precalc_3Dz" class="py-name" href="#" onclick="return doclink('link-157', 'implicit_precalc_3Dz', 'link-157');">implicit_precalc_3Dz</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">az</tt><tt class="py-op">,</tt> <tt class="py-name">bz</tt><tt class="py-op">,</tt> <tt class="py-name">cz</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">)</tt> </tt>
<a name="L697"></a><tt class="py-lineno">697</tt>  <tt class="py-line">        <tt class="py-name">current_t</tt> <tt class="py-op">+=</tt> <tt class="py-name">this_dt</tt> </tt>
<a name="L698"></a><tt class="py-lineno">698</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="L699"></a><tt class="py-lineno">699</tt>  <tt class="py-line"> </tt>
<a name="_Vfunc_X"></a><div id="_Vfunc_X-def"><a name="L700"></a><tt class="py-lineno">700</tt> <a class="py-toggle" href="#" id="_Vfunc_X-toggle" onclick="return toggle('_Vfunc_X');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_Vfunc_X">_Vfunc_X</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">nu</tt><tt class="py-op">,</tt> <tt class="py-param">beta</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Vfunc_X-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_Vfunc_X-expanded"><a name="L701"></a><tt class="py-lineno">701</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-number">1.</tt><tt class="py-op">/</tt><tt class="py-name">nu</tt> <tt class="py-op">*</tt> <tt class="py-name">x</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">beta</tt><tt class="py-op">+</tt><tt class="py-number">4.</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-name">beta</tt><tt class="py-op">+</tt><tt class="py-number">1.</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">9.</tt><tt class="py-op">*</tt><tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
</div><a name="_Mfunc1D_X"></a><div id="_Mfunc1D_X-def"><a name="L702"></a><tt class="py-lineno">702</tt> <a class="py-toggle" href="#" id="_Mfunc1D_X-toggle" onclick="return toggle('_Mfunc1D_X');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_Mfunc1D_X">_Mfunc1D_X</a><tt class="py-op">(</tt><tt class="py-param">x</tt><tt class="py-op">,</tt> <tt class="py-param">gamma</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">,</tt> <tt class="py-param">beta</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_Mfunc1D_X-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_Mfunc1D_X-expanded"><a name="L703"></a><tt class="py-lineno">703</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">gamma</tt> <tt class="py-op">*</tt> <tt class="py-number">4.</tt><tt class="py-op">/</tt><tt class="py-number">3.</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-number">0.5</tt><tt class="py-op">+</tt><tt class="py-name">h</tt><tt class="py-op">+</tt><tt class="py-name">x</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">h</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> <tt class="py-op">*</tt> <tt class="py-name">x</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">x</tt><tt class="py-op">)</tt> </tt>
</div><a name="_inject_mutations_1D_X"></a><div id="_inject_mutations_1D_X-def"><a name="L704"></a><tt class="py-lineno">704</tt> <a class="py-toggle" href="#" id="_inject_mutations_1D_X-toggle" onclick="return toggle('_inject_mutations_1D_X');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_inject_mutations_1D_X">_inject_mutations_1D_X</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">dt</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">,</tt> <tt class="py-param">beta</tt><tt class="py-op">,</tt> <tt class="py-param">alpha</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_inject_mutations_1D_X-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_inject_mutations_1D_X-expanded"><a name="L705"></a><tt class="py-lineno">705</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L706"></a><tt class="py-lineno">706</tt>  <tt class="py-line"><tt class="py-docstring">    Inject novel mutations for a timestep.</tt> </tt>
<a name="L707"></a><tt class="py-lineno">707</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L708"></a><tt class="py-lineno">708</tt>  <tt class="py-line">    <tt class="py-name">factor</tt> <tt class="py-op">=</tt> <tt class="py-number">2.</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">1.</tt><tt class="py-op">+</tt><tt class="py-number">2.</tt><tt class="py-op">*</tt><tt class="py-name">beta</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-number">1.</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-name">alpha</tt><tt class="py-op">+</tt><tt class="py-number">1.</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">beta</tt><tt class="py-op">)</tt>  </tt>
<a name="L709"></a><tt class="py-lineno">709</tt>  <tt class="py-line">    <tt class="py-name">phi</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dt</tt><tt class="py-op">/</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">*</tt> <tt class="py-name">theta0</tt><tt class="py-op">/</tt><tt class="py-number">2.</tt> <tt class="py-op">*</tt> <tt class="py-name">factor</tt> <tt class="py-op">*</tt> <tt class="py-number">2.</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">2</tt><tt class="py-op">]</tt> <tt class="py-op">-</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt> </tt>
<a name="L710"></a><tt class="py-lineno">710</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="L711"></a><tt class="py-lineno">711</tt>  <tt class="py-line"> </tt>
<a name="one_pop_X"></a><div id="one_pop_X-def"><a name="L712"></a><tt class="py-lineno">712</tt> <a class="py-toggle" href="#" id="one_pop_X-toggle" onclick="return toggle('one_pop_X');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#one_pop_X">one_pop_X</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">T</tt><tt class="py-op">,</tt> <tt class="py-param">nu</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">gamma</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">beta</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">alpha</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">theta0</tt><tt class="py-op">=</tt><tt class="py-number">1.0</tt><tt class="py-op">,</tt>  </tt>
<a name="L713"></a><tt class="py-lineno">713</tt>  <tt class="py-line">              <tt class="py-param">initial_t</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">frozen</tt><tt class="py-op">=</tt><tt class="py-name">False</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="one_pop_X-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="one_pop_X-expanded"><a name="L714"></a><tt class="py-lineno">714</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L715"></a><tt class="py-lineno">715</tt>  <tt class="py-line"><tt class="py-docstring">    Integrate a 1-dimensional phi foward.</tt> </tt>
<a name="L716"></a><tt class="py-lineno">716</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L717"></a><tt class="py-lineno">717</tt>  <tt class="py-line"><tt class="py-docstring">    phi: Initial 1-dimensional phi</tt> </tt>
<a name="L718"></a><tt class="py-lineno">718</tt>  <tt class="py-line"><tt class="py-docstring">    xx: Grid upon (0,1) overwhich phi is defined.</tt> </tt>
<a name="L719"></a><tt class="py-lineno">719</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L720"></a><tt class="py-lineno">720</tt>  <tt class="py-line"><tt class="py-docstring">    nu, gamma, and theta0 may be functions of time.</tt> </tt>
<a name="L721"></a><tt class="py-lineno">721</tt>  <tt class="py-line"><tt class="py-docstring">    nu: Population size</tt> </tt>
<a name="L722"></a><tt class="py-lineno">722</tt>  <tt class="py-line"><tt class="py-docstring">    gamma: Scaled selection coefficient on *all* segregating alleles</tt> </tt>
<a name="L723"></a><tt class="py-lineno">723</tt>  <tt class="py-line"><tt class="py-docstring">    h: Dominance coefficient. h = 0.5 corresponds to genic selection. </tt> </tt>
<a name="L724"></a><tt class="py-lineno">724</tt>  <tt class="py-line"><tt class="py-docstring">       Heterozygous females have fitness 1+2sh and homozygous females have</tt> </tt>
<a name="L725"></a><tt class="py-lineno">725</tt>  <tt class="py-line"><tt class="py-docstring">       fitness 1+2s. Male carriers have fitness 1+2s.</tt> </tt>
<a name="L726"></a><tt class="py-lineno">726</tt>  <tt class="py-line"><tt class="py-docstring">    theta0: Propotional to ancestral size. Typically constant.</tt> </tt>
<a name="L727"></a><tt class="py-lineno">727</tt>  <tt class="py-line"><tt class="py-docstring">    beta: Breeding ratio, beta=Nf/Nm.</tt> </tt>
<a name="L728"></a><tt class="py-lineno">728</tt>  <tt class="py-line"><tt class="py-docstring">    alpha: Male to female mutation rate ratio, beta = mu_m / mu_f.</tt> </tt>
<a name="L729"></a><tt class="py-lineno">729</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L730"></a><tt class="py-lineno">730</tt>  <tt class="py-line"><tt class="py-docstring">    T: Time at which to halt integration</tt> </tt>
<a name="L731"></a><tt class="py-lineno">731</tt>  <tt class="py-line"><tt class="py-docstring">    initial_t: Time at which to start integration. (Note that this only matters</tt> </tt>
<a name="L732"></a><tt class="py-lineno">732</tt>  <tt class="py-line"><tt class="py-docstring">               if one of the demographic parameters is a function of time.)</tt> </tt>
<a name="L733"></a><tt class="py-lineno">733</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L734"></a><tt class="py-lineno">734</tt>  <tt class="py-line"><tt class="py-docstring">    frozen: If True, population is 'frozen' so that it does not change.</tt> </tt>
<a name="L735"></a><tt class="py-lineno">735</tt>  <tt class="py-line"><tt class="py-docstring">            In the one_pop case, this is equivalent to not running the</tt> </tt>
<a name="L736"></a><tt class="py-lineno">736</tt>  <tt class="py-line"><tt class="py-docstring">            integration at all.</tt> </tt>
<a name="L737"></a><tt class="py-lineno">737</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L738"></a><tt class="py-lineno">738</tt>  <tt class="py-line">    <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">copy</tt><tt class="py-op">(</tt><tt class="py-op">)</tt> </tt>
<a name="L739"></a><tt class="py-lineno">739</tt>  <tt class="py-line"> </tt>
<a name="L740"></a><tt class="py-lineno">740</tt>  <tt class="py-line">    <tt class="py-comment"># For a one population integration, freezing means just not integrating.</tt> </tt>
<a name="L741"></a><tt class="py-lineno">741</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">frozen</tt><tt class="py-op">:</tt> </tt>
<a name="L742"></a><tt class="py-lineno">742</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
<a name="L743"></a><tt class="py-lineno">743</tt>  <tt class="py-line"> </tt>
<a name="L744"></a><tt class="py-lineno">744</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">initial_t</tt> <tt class="py-op">==</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L745"></a><tt class="py-lineno">745</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
<a name="L746"></a><tt class="py-lineno">746</tt>  <tt class="py-line">    <tt class="py-keyword">elif</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">initial_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-number">0</tt><tt class="py-op">:</tt> </tt>
<a name="L747"></a><tt class="py-lineno">747</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'Final integration time T (%f) is less than '</tt> </tt>
<a name="L748"></a><tt class="py-lineno">748</tt>  <tt class="py-line">                         <tt class="py-string">'intial_time (%f). Integration cannot be run '</tt> </tt>
<a name="L749"></a><tt class="py-lineno">749</tt>  <tt class="py-line">                         <tt class="py-string">'backwards.'</tt> <tt class="py-op">%</tt> <tt class="py-op">(</tt><tt class="py-name">T</tt><tt class="py-op">,</tt> <tt class="py-name">initial_t</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L750"></a><tt class="py-lineno">750</tt>  <tt class="py-line"> </tt>
<a name="L751"></a><tt class="py-lineno">751</tt>  <tt class="py-line">    <tt class="py-name">vars_to_check</tt> <tt class="py-op">=</tt> <tt class="py-op">(</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">,</tt> <tt class="py-name">alpha</tt><tt class="py-op">)</tt> </tt>
<a name="L752"></a><tt class="py-lineno">752</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">all</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">isscalar</tt><tt class="py-op">(</tt><tt class="py-name">var</tt><tt class="py-op">)</tt> <tt class="py-keyword">for</tt> <tt class="py-name">var</tt> <tt class="py-keyword">in</tt> <tt class="py-name">vars_to_check</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L753"></a><tt class="py-lineno">753</tt>  <tt class="py-line">        <tt class="py-keyword">return</tt> <tt id="link-158" class="py-name" targets="Function dadi.Integration._one_pop_const_params_X()=dadi.Integration-module.html#_one_pop_const_params_X"><a title="dadi.Integration._one_pop_const_params_X" class="py-name" href="#" onclick="return doclink('link-158', '_one_pop_const_params_X', 'link-158');">_one_pop_const_params_X</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt><tt class="py-op">,</tt> <tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">,</tt> <tt class="py-name">alpha</tt><tt class="py-op">,</tt>  </tt>
<a name="L754"></a><tt class="py-lineno">754</tt>  <tt class="py-line">                                       <tt class="py-name">theta0</tt><tt class="py-op">,</tt> <tt class="py-name">initial_t</tt><tt class="py-op">)</tt> </tt>
<a name="L755"></a><tt class="py-lineno">755</tt>  <tt class="py-line">    <tt class="py-keyword">else</tt><tt class="py-op">:</tt> </tt>
<a name="L756"></a><tt class="py-lineno">756</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">NotImplementedError</tt><tt class="py-op">(</tt><tt class="py-string">'X chromosome integration currently only '</tt> </tt>
<a name="L757"></a><tt class="py-lineno">757</tt>  <tt class="py-line">                                  <tt class="py-string">'implemented for constant parameters.'</tt><tt class="py-op">)</tt> </tt>
</div><a name="L758"></a><tt class="py-lineno">758</tt>  <tt class="py-line"> </tt>
<a name="_one_pop_const_params_X"></a><div id="_one_pop_const_params_X-def"><a name="L759"></a><tt class="py-lineno">759</tt> <a class="py-toggle" href="#" id="_one_pop_const_params_X-toggle" onclick="return toggle('_one_pop_const_params_X');">-</a><tt class="py-line"><tt class="py-keyword">def</tt> <a class="py-def-name" href="dadi.Integration-module.html#_one_pop_const_params_X">_one_pop_const_params_X</a><tt class="py-op">(</tt><tt class="py-param">phi</tt><tt class="py-op">,</tt> <tt class="py-param">xx</tt><tt class="py-op">,</tt> <tt class="py-param">T</tt><tt class="py-op">,</tt> <tt class="py-param">nu</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">gamma</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">,</tt> <tt class="py-param">h</tt><tt class="py-op">=</tt><tt class="py-number">0.5</tt><tt class="py-op">,</tt> <tt class="py-param">beta</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">alpha</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt>  </tt>
<a name="L760"></a><tt class="py-lineno">760</tt>  <tt class="py-line">                            <tt class="py-param">theta0</tt><tt class="py-op">=</tt><tt class="py-number">1</tt><tt class="py-op">,</tt> <tt class="py-param">initial_t</tt><tt class="py-op">=</tt><tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
</div><div id="_one_pop_const_params_X-collapsed" style="display:none;" pad="+++" indent="++++"></div><div id="_one_pop_const_params_X-expanded"><a name="L761"></a><tt class="py-lineno">761</tt>  <tt class="py-line">    <tt class="py-docstring">"""</tt> </tt>
<a name="L762"></a><tt class="py-lineno">762</tt>  <tt class="py-line"><tt class="py-docstring">    Integrate one population with constant parameters.</tt> </tt>
<a name="L763"></a><tt class="py-lineno">763</tt>  <tt class="py-line"><tt class="py-docstring"></tt> </tt>
<a name="L764"></a><tt class="py-lineno">764</tt>  <tt class="py-line"><tt class="py-docstring">    In this case, we can precompute our a,b,c matrices for the linear system</tt> </tt>
<a name="L765"></a><tt class="py-lineno">765</tt>  <tt class="py-line"><tt class="py-docstring">    we need to evolve. This we can efficiently do in Python, rather than </tt> </tt>
<a name="L766"></a><tt class="py-lineno">766</tt>  <tt class="py-line"><tt class="py-docstring">    relying on C. The nice thing is that the Python is much faster to debug.</tt> </tt>
<a name="L767"></a><tt class="py-lineno">767</tt>  <tt class="py-line"><tt class="py-docstring">    """</tt> </tt>
<a name="L768"></a><tt class="py-lineno">768</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">less</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">T</tt><tt class="py-op">,</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt><tt class="py-name">theta0</tt><tt class="py-op">,</tt><tt class="py-name">beta</tt><tt class="py-op">,</tt><tt class="py-name">alpha</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L769"></a><tt class="py-lineno">769</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A time, population size, migration rate, theta0, '</tt> </tt>
<a name="L770"></a><tt class="py-lineno">770</tt>  <tt class="py-line">                         <tt class="py-string">'beta, or alpha is &lt; 0. Has the model been '</tt> </tt>
<a name="L771"></a><tt class="py-lineno">771</tt>  <tt class="py-line">                         <tt class="py-string">'mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L772"></a><tt class="py-lineno">772</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">any</tt><tt class="py-op">(</tt><tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">equal</tt><tt class="py-op">(</tt><tt class="py-op">[</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt><tt class="py-name">beta</tt><tt class="py-op">]</tt><tt class="py-op">,</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L773"></a><tt class="py-lineno">773</tt>  <tt class="py-line">        <tt class="py-keyword">raise</tt> <tt class="py-name">ValueError</tt><tt class="py-op">(</tt><tt class="py-string">'A population size or beta is 0. Has the model been '</tt> </tt>
<a name="L774"></a><tt class="py-lineno">774</tt>  <tt class="py-line">                         <tt class="py-string">'mis-specified?'</tt><tt class="py-op">)</tt> </tt>
<a name="L775"></a><tt class="py-lineno">775</tt>  <tt class="py-line"> </tt>
<a name="L776"></a><tt class="py-lineno">776</tt>  <tt class="py-line">    <tt class="py-name">M</tt> <tt class="py-op">=</tt> <tt id="link-159" class="py-name" targets="Function dadi.Integration._Mfunc1D_X()=dadi.Integration-module.html#_Mfunc1D_X"><a title="dadi.Integration._Mfunc1D_X" class="py-name" href="#" onclick="return doclink('link-159', '_Mfunc1D_X', 'link-159');">_Mfunc1D_X</a></tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
<a name="L777"></a><tt class="py-lineno">777</tt>  <tt class="py-line">    <tt class="py-name">MInt</tt> <tt class="py-op">=</tt> <tt id="link-160" class="py-name"><a title="dadi.Integration._Mfunc1D_X" class="py-name" href="#" onclick="return doclink('link-160', '_Mfunc1D_X', 'link-159');">_Mfunc1D_X</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">gamma</tt><tt class="py-op">,</tt> <tt class="py-name">h</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
<a name="L778"></a><tt class="py-lineno">778</tt>  <tt class="py-line">    <tt class="py-name">V</tt> <tt class="py-op">=</tt> <tt id="link-161" class="py-name" targets="Function dadi.Integration._Vfunc_X()=dadi.Integration-module.html#_Vfunc_X"><a title="dadi.Integration._Vfunc_X" class="py-name" href="#" onclick="return doclink('link-161', '_Vfunc_X', 'link-161');">_Vfunc_X</a></tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
<a name="L779"></a><tt class="py-lineno">779</tt>  <tt class="py-line">    <tt class="py-name">VInt</tt> <tt class="py-op">=</tt> <tt id="link-162" class="py-name"><a title="dadi.Integration._Vfunc_X" class="py-name" href="#" onclick="return doclink('link-162', '_Vfunc_X', 'link-161');">_Vfunc_X</a></tt><tt class="py-op">(</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+</tt> <tt class="py-name">xx</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">/</tt><tt class="py-number">2</tt><tt class="py-op">,</tt> <tt class="py-name">nu</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">)</tt> </tt>
<a name="L780"></a><tt class="py-lineno">780</tt>  <tt class="py-line"> </tt>
<a name="L781"></a><tt class="py-lineno">781</tt>  <tt class="py-line">    <tt class="py-name">dx</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">diff</tt><tt class="py-op">(</tt><tt class="py-name">xx</tt><tt class="py-op">)</tt> </tt>
<a name="L782"></a><tt class="py-lineno">782</tt>  <tt class="py-line">    <tt class="py-name">dfactor</tt> <tt class="py-op">=</tt> <tt id="link-163" class="py-name"><a title="dadi.Integration._compute_dfactor" class="py-name" href="#" onclick="return doclink('link-163', '_compute_dfactor', 'link-110');">_compute_dfactor</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt> </tt>
<a name="L783"></a><tt class="py-lineno">783</tt>  <tt class="py-line">    <tt class="py-name">delj</tt> <tt class="py-op">=</tt> <tt id="link-164" class="py-name"><a title="dadi.Integration._compute_delj" class="py-name" href="#" onclick="return doclink('link-164', '_compute_delj', 'link-111');">_compute_delj</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt> <tt class="py-name">MInt</tt><tt class="py-op">,</tt> <tt class="py-name">VInt</tt><tt class="py-op">)</tt> </tt>
<a name="L784"></a><tt class="py-lineno">784</tt>  <tt class="py-line"> </tt>
<a name="L785"></a><tt class="py-lineno">785</tt>  <tt class="py-line">    <tt class="py-name">a</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> </tt>
<a name="L786"></a><tt class="py-lineno">786</tt>  <tt class="py-line">    <tt class="py-name">a</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MInt</tt> <tt class="py-op">*</tt> <tt class="py-name">delj</tt> <tt class="py-op">-</tt> <tt class="py-name">V</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L787"></a><tt class="py-lineno">787</tt>  <tt class="py-line"> </tt>
<a name="L788"></a><tt class="py-lineno">788</tt>  <tt class="py-line">    <tt class="py-name">c</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> </tt>
<a name="L789"></a><tt class="py-lineno">789</tt>  <tt class="py-line">    <tt class="py-name">c</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MInt</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">delj</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">V</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L790"></a><tt class="py-lineno">790</tt>  <tt class="py-line"> </tt>
<a name="L791"></a><tt class="py-lineno">791</tt>  <tt class="py-line">    <tt class="py-name">b</tt> <tt class="py-op">=</tt> <tt class="py-name">numpy</tt><tt class="py-op">.</tt><tt class="py-name">zeros</tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">.</tt><tt class="py-name">shape</tt><tt class="py-op">)</tt> </tt>
<a name="L792"></a><tt class="py-lineno">792</tt>  <tt class="py-line">    <tt class="py-name">b</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MInt</tt> <tt class="py-op">*</tt> <tt class="py-name">delj</tt> <tt class="py-op">-</tt> <tt class="py-name">V</tt><tt class="py-op">[</tt><tt class="py-op">:</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L793"></a><tt class="py-lineno">793</tt>  <tt class="py-line">    <tt class="py-name">b</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-name">dfactor</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">*</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-name">MInt</tt> <tt class="py-op">*</tt> <tt class="py-op">(</tt><tt class="py-number">1</tt><tt class="py-op">-</tt><tt class="py-name">delj</tt><tt class="py-op">)</tt> <tt class="py-op">+</tt> <tt class="py-name">V</tt><tt class="py-op">[</tt><tt class="py-number">1</tt><tt class="py-op">:</tt><tt class="py-op">]</tt><tt class="py-op">/</tt><tt class="py-op">(</tt><tt class="py-number">2</tt><tt class="py-op">*</tt><tt class="py-name">dx</tt><tt class="py-op">)</tt><tt class="py-op">)</tt> </tt>
<a name="L794"></a><tt class="py-lineno">794</tt>  <tt class="py-line"> </tt>
<a name="L795"></a><tt class="py-lineno">795</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt><tt class="py-op">(</tt><tt class="py-name">M</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">&lt;=</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L796"></a><tt class="py-lineno">796</tt>  <tt class="py-line">        <tt class="py-name">b</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">(</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu</tt> <tt class="py-op">-</tt> <tt class="py-name">M</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt> </tt>
<a name="L797"></a><tt class="py-lineno">797</tt>  <tt class="py-line">    <tt class="py-keyword">if</tt><tt class="py-op">(</tt><tt class="py-name">M</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">&gt;=</tt> <tt class="py-number">0</tt><tt class="py-op">)</tt><tt class="py-op">:</tt> </tt>
<a name="L798"></a><tt class="py-lineno">798</tt>  <tt class="py-line">        <tt class="py-name">b</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> <tt class="py-op">+=</tt> <tt class="py-op">-</tt><tt class="py-op">(</tt><tt class="py-op">-</tt><tt class="py-number">0.5</tt><tt class="py-op">/</tt><tt class="py-name">nu</tt> <tt class="py-op">-</tt> <tt class="py-name">M</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt><tt class="py-op">)</tt><tt class="py-op">*</tt><tt class="py-number">2</tt><tt class="py-op">/</tt><tt class="py-name">dx</tt><tt class="py-op">[</tt><tt class="py-op">-</tt><tt class="py-number">1</tt><tt class="py-op">]</tt> </tt>
<a name="L799"></a><tt class="py-lineno">799</tt>  <tt class="py-line"> </tt>
<a name="L800"></a><tt class="py-lineno">800</tt>  <tt class="py-line">    <tt class="py-name">dt</tt> <tt class="py-op">=</tt> <tt id="link-165" class="py-name"><a title="dadi.Integration._compute_dt" class="py-name" href="#" onclick="return doclink('link-165', '_compute_dt', 'link-28');">_compute_dt</a></tt><tt class="py-op">(</tt><tt class="py-name">dx</tt><tt class="py-op">,</tt><tt class="py-name">nu</tt><tt class="py-op">,</tt><tt class="py-op">[</tt><tt class="py-number">0</tt><tt class="py-op">]</tt><tt class="py-op">,</tt><tt class="py-name">gamma</tt><tt class="py-op">,</tt><tt class="py-name">h</tt><tt class="py-op">)</tt> </tt>
<a name="L801"></a><tt class="py-lineno">801</tt>  <tt class="py-line">    <tt class="py-name">current_t</tt> <tt class="py-op">=</tt> <tt class="py-name">initial_t</tt> </tt>
<a name="L802"></a><tt class="py-lineno">802</tt>  <tt class="py-line">    <tt class="py-keyword">while</tt> <tt class="py-name">current_t</tt> <tt class="py-op">&lt;</tt> <tt class="py-name">T</tt><tt class="py-op">:</tt>     </tt>
<a name="L803"></a><tt class="py-lineno">803</tt>  <tt class="py-line">        <tt class="py-name">this_dt</tt> <tt class="py-op">=</tt> <tt class="py-name">min</tt><tt class="py-op">(</tt><tt class="py-name">dt</tt><tt class="py-op">,</tt> <tt class="py-name">T</tt> <tt class="py-op">-</tt> <tt class="py-name">current_t</tt><tt class="py-op">)</tt> </tt>
<a name="L804"></a><tt class="py-lineno">804</tt>  <tt class="py-line"> </tt>
<a name="L805"></a><tt class="py-lineno">805</tt>  <tt class="py-line">        <tt id="link-166" class="py-name" targets="Function dadi.Integration._inject_mutations_1D_X()=dadi.Integration-module.html#_inject_mutations_1D_X"><a title="dadi.Integration._inject_mutations_1D_X" class="py-name" href="#" onclick="return doclink('link-166', '_inject_mutations_1D_X', 'link-166');">_inject_mutations_1D_X</a></tt><tt class="py-op">(</tt><tt class="py-name">phi</tt><tt class="py-op">,</tt> <tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt class="py-name">xx</tt><tt class="py-op">,</tt> <tt class="py-name">theta0</tt><tt class="py-op">,</tt> <tt class="py-name">beta</tt><tt class="py-op">,</tt> <tt class="py-name">alpha</tt><tt class="py-op">)</tt> </tt>
<a name="L806"></a><tt class="py-lineno">806</tt>  <tt class="py-line">        <tt class="py-name">r</tt> <tt class="py-op">=</tt> <tt class="py-name">phi</tt><tt class="py-op">/</tt><tt class="py-name">this_dt</tt> </tt>
<a name="L807"></a><tt class="py-lineno">807</tt>  <tt class="py-line">        <tt class="py-name">phi</tt> <tt class="py-op">=</tt> <tt id="link-167" class="py-name"><a title="dadi.tridiag
dadi.tridiag.tridiag" class="py-name" href="#" onclick="return doclink('link-167', 'tridiag', 'link-4');">tridiag</a></tt><tt class="py-op">.</tt><tt id="link-168" class="py-name"><a title="dadi.tridiag
dadi.tridiag.tridiag" class="py-name" href="#" onclick="return doclink('link-168', 'tridiag', 'link-4');">tridiag</a></tt><tt class="py-op">(</tt><tt class="py-name">a</tt><tt class="py-op">,</tt> <tt class="py-name">b</tt><tt class="py-op">+</tt><tt class="py-number">1.</tt><tt class="py-op">/</tt><tt class="py-name">this_dt</tt><tt class="py-op">,</tt> <tt class="py-name">c</tt><tt class="py-op">,</tt> <tt class="py-name">r</tt><tt class="py-op">)</tt> </tt>
<a name="L808"></a><tt class="py-lineno">808</tt>  <tt class="py-line">        <tt class="py-name">current_t</tt> <tt class="py-op">+=</tt> <tt class="py-name">this_dt</tt> </tt>
<a name="L809"></a><tt class="py-lineno">809</tt>  <tt class="py-line">    <tt class="py-keyword">return</tt> <tt class="py-name">phi</tt> </tt>
</div><a name="L810"></a><tt class="py-lineno">810</tt>  <tt class="py-line"> </tt><script type="text/javascript">
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